GCSE Maths: Simplifying: collecting like terms (Foundation)
Part of the GCSE Maths algebra basics chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Simplifying: collecting like terms
To simplify an expression means to write it in a shorter, neater way without changing its value. The most important way to do that is collecting like terms.
Think about fruit. 3 apples and 2 apples make 5 apples. But 3 apples and 2 pears do not make 5 of anything useful; you just have “3 apples and 2 pears”. Algebra works in exactly the same way. The terms 3x and 2x are the same kind of thing (lots of x), so we can add them: 3x + 2x = 5x. But 3x + 2y cannot be simplified, because x and y are different things.
Like terms have exactly the same letters, with exactly the same powers. The number in front (the coefficient) can be different.
| Like terms (can be added) | Unlike terms (cannot be added) |
|---|---|
| 3x and 7x | 3x and 7y (different letters) |
| 5x2 and −x2 | 5x2 and 5x (different powers) |
| 4ab and 9ba (the order of letters does not matter) | 4ab and 4a (one has a b, one does not) |
| 6 and −2 (plain numbers) | 6 and 6x (one has a letter) |
Method. (1) Underline or circle each term, with the sign in front of it. (2) Group the like terms together. (3) Add or subtract the coefficients. A letter on its own, like x, has a coefficient of 1.
Key ideas
- Like terms have the same letters with the same powers. 3x and 5x are like; 3x and 5x2 are not.
- Add the coefficients and keep the letters: 3x + 5x = 8x (the x does not change).
- The sign in front of a term belongs to the term: in 7x − 3y the terms are +7x and −3y.
- x means 1x, so x + 4x = 5x. And −x means −1x.
- xy and yx are the same term (multiplication can be done in any order).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+3x, +5x, −2x
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x terms: +3x, +5x, −2x
add the coefficients: 3 + 5 − 2 = 6 so they give 6x - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.6x
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives 18 and the answer gives 18. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+4a, +3b, −a, +5b, −2, +7
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.a terms: +4a, −a
add the coefficients: 4 − 1 = 3 so they give 3a
b terms: +3b, +5b
add the coefficients: 3 + 5 = 8 so they give 8b
number terms: −2, +7
add the coefficients: −2 + 7 = 5 so they give 5 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.3a + 8b + 5
Check. Test with numbers. Put a = 3, b = 4 into the original and into your answer. The original gives 46 and the answer gives 46. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+3x2, +2x, −x2, +5x, −4
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x2 terms: +3x2, −x2
add the coefficients: 3 − 1 = 2 so they give 2x2
x terms: +2x, +5x
add the coefficients: 2 + 5 = 7 so they give 7x
number terms: −4 (only one of this type, so it stays as it is) - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.2x2 + 7x − 4
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives 35 and the answer gives 35. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+4ab, −7ab, +2a2, +ab
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.a2 terms: +2a2 (only one of this type, so it stays as it is)
ab terms: +4ab, −7ab, +ab
add the coefficients: 4 − 7 + 1 = −2 so they give −2ab - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.2a2 − 2ab
Check. Test with numbers. Put a = 3, b = 4 into the original and into your answer. The original gives −6 and the answer gives −6. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Watch out
x and x2 are different kinds of term, so 3x + 2x2 cannot be simplified to 5x3 or 5x2. Also watch the signs: in 5x − 2x + 3 the term being added to 5x is −2x.Exercise 7B Collecting like terms
Non-calculatorKey words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+3x, +4x
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x terms: +3x, +4x
add the coefficients: 3 + 4 = 7 so they give 7x - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.7x
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives 21 and the answer gives 21. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+9y, −2y
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.y terms: +9y, −2y
add the coefficients: 9 − 2 = 7 so they give 7y - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.7y
Check. Test with numbers. Put y = 3 into the original and into your answer. The original gives 21 and the answer gives 21. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+5a, +a
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.a terms: +5a, +a
add the coefficients: 5 + 1 = 6 so they give 6a - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.6a
Check. Test with numbers. Put a = 3 into the original and into your answer. The original gives 18 and the answer gives 18. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+8m, −3m
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.m terms: +8m, −3m
add the coefficients: 8 − 3 = 5 so they give 5m - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.5m
Check. Test with numbers. Put m = 3 into the original and into your answer. The original gives 15 and the answer gives 15. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+6p, −p, −2p
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.p terms: +6p, −p, −2p
add the coefficients: 6 − 1 − 2 = 3 so they give 3p - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.3p
Check. Test with numbers. Put p = 3 into the original and into your answer. The original gives 9 and the answer gives 9. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+7t, +2t, −4t
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.t terms: +7t, +2t, −4t
add the coefficients: 7 + 2 − 4 = 5 so they give 5t - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.5t
Check. Test with numbers. Put t = 3 into the original and into your answer. The original gives 15 and the answer gives 15. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+2x, +3, +5x, +4
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x terms: +2x, +5x
add the coefficients: 2 + 5 = 7 so they give 7x
number terms: +3, +4
add the coefficients: 3 + 4 = 7 so they give 7 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.7x + 7
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives 28 and the answer gives 28. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+7y, +2, −3y, +5
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.y terms: +7y, −3y
add the coefficients: 7 − 3 = 4 so they give 4y
number terms: +2, +5
add the coefficients: 2 + 5 = 7 so they give 7 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.4y + 7
Check. Test with numbers. Put y = 3 into the original and into your answer. The original gives 19 and the answer gives 19. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+4a, −1, +a, −6
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.a terms: +4a, +a
add the coefficients: 4 + 1 = 5 so they give 5a
number terms: −1, −6
add the coefficients: −1 − 6 = −7 so they give −7 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.5a − 7
Check. Test with numbers. Put a = 3 into the original and into your answer. The original gives 8 and the answer gives 8. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+10, +3b, −4, +2b
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.b terms: +3b, +2b
add the coefficients: 3 + 2 = 5 so they give 5b
number terms: +10, −4
add the coefficients: 10 − 4 = 6 so they give 6 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.5b + 6
Check. Test with numbers. Put b = 3 into the original and into your answer. The original gives 21 and the answer gives 21. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+3a, +2b, +4a, +5b
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.a terms: +3a, +4a
add the coefficients: 3 + 4 = 7 so they give 7a
b terms: +2b, +5b
add the coefficients: 2 + 5 = 7 so they give 7b - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.7a + 7b
Check. Test with numbers. Put a = 3, b = 4 into the original and into your answer. The original gives 49 and the answer gives 49. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+5x, +2y, −2x, +3y
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x terms: +5x, −2x
add the coefficients: 5 − 2 = 3 so they give 3x
y terms: +2y, +3y
add the coefficients: 2 + 3 = 5 so they give 5y - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.3x + 5y
Check. Test with numbers. Put x = 3, y = 4 into the original and into your answer. The original gives 29 and the answer gives 29. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+6p, −3q, +p, +4q
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.p terms: +6p, +p
add the coefficients: 6 + 1 = 7 so they give 7p
q terms: −3q, +4q
add the coefficients: −3 + 4 = 1 so they give q - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.7p + q
Check. Test with numbers. Put p = 3, q = 4 into the original and into your answer. The original gives 25 and the answer gives 25. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+7m, −2n, −3m, −n
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.m terms: +7m, −3m
add the coefficients: 7 − 3 = 4 so they give 4m
n terms: −2n, −n
add the coefficients: −2 − 1 = −3 so they give −3n - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.4m − 3n
Check. Test with numbers. Put m = 3, n = 4 into the original and into your answer. The original gives 0 and the answer gives 0. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)−3x, +7x, +2
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x terms: −3x, +7x
add the coefficients: −3 + 7 = 4 so they give 4x
number terms: +2 (only one of this type, so it stays as it is) - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.4x + 2
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives 14 and the answer gives 14. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+2a, −5a, +4
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.a terms: +2a, −5a
add the coefficients: 2 − 5 = −3 so they give −3a
number terms: +4 (only one of this type, so it stays as it is) - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.−3a + 4
Check. Test with numbers. Put a = 3 into the original and into your answer. The original gives −5 and the answer gives −5. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+x, −6, −3x, +2
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x terms: +x, −3x
add the coefficients: 1 − 3 = −2 so they give −2x
number terms: −6, +2
add the coefficients: −6 + 2 = −4 so they give −4 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.−2x − 4
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives −10 and the answer gives −10. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)−2y, −3y, +9
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.y terms: −2y, −3y
add the coefficients: −2 − 3 = −5 so they give −5y
number terms: +9 (only one of this type, so it stays as it is) - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.−5y + 9
Check. Test with numbers. Put y = 3 into the original and into your answer. The original gives −6 and the answer gives −6. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+x2, +3x, +2x2, +x
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x2 terms: +x2, +2x2
add the coefficients: 1 + 2 = 3 so they give 3x2
x terms: +3x, +x
add the coefficients: 3 + 1 = 4 so they give 4x - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.3x2 + 4x
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives 39 and the answer gives 39. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+3x2, +5, −x2, −2
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x2 terms: +3x2, −x2
add the coefficients: 3 − 1 = 2 so they give 2x2
number terms: +5, −2
add the coefficients: 5 − 2 = 3 so they give 3 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.2x2 + 3
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives 21 and the answer gives 21. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+4a2, −a, +a2, +6a
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.a2 terms: +4a2, +a2
add the coefficients: 4 + 1 = 5 so they give 5a2
a terms: −a, +6a
add the coefficients: −1 + 6 = 5 so they give 5a - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.5a2 + 5a
Check. Test with numbers. Put a = 3 into the original and into your answer. The original gives 60 and the answer gives 60. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+5y2, +2y, −4y2, −7y
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.y2 terms: +5y2, −4y2
add the coefficients: 5 − 4 = 1 so they give y2
y terms: +2y, −7y
add the coefficients: 2 − 7 = −5 so they give −5y - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.y2 − 5y
Check. Test with numbers. Put y = 3 into the original and into your answer. The original gives −6 and the answer gives −6. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+3xy, +2xy
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.xy terms: +3xy, +2xy
add the coefficients: 3 + 2 = 5 so they give 5xy - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.5xy
Check. Test with numbers. Put x = 3, y = 4 into the original and into your answer. The original gives 60 and the answer gives 60. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+5ab, −2ab
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.ab terms: +5ab, −2ab
add the coefficients: 5 − 2 = 3 so they give 3ab - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.3ab
Check. Test with numbers. Put a = 3, b = 4 into the original and into your answer. The original gives 36 and the answer gives 36. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+4pq, +p, +3pq, −p
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.pq terms: +4pq, +3pq
add the coefficients: 4 + 3 = 7 so they give 7pq
p terms: +p, −p
add the coefficients: 1 − 1 = 0 so they cancel to give 0 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.7pq
Check. Test with numbers. Put p = 3, q = 4 into the original and into your answer. The original gives 84 and the answer gives 84. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+2xy, +3x, +5xy, −x
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.xy terms: +2xy, +5xy
add the coefficients: 2 + 5 = 7 so they give 7xy
x terms: +3x, −x
add the coefficients: 3 − 1 = 2 so they give 2x - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.7xy + 2x
Check. Test with numbers. Put x = 3, y = 4 into the original and into your answer. The original gives 90 and the answer gives 90. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+3x, +2, +x, +5, +3x, +2, +x, +5
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.x terms: +3x, +x, +3x, +x
add the coefficients: 3 + 1 + 3 + 1 = 8 so they give 8x
number terms: +2, +5, +2, +5
add the coefficients: 2 + 5 + 2 + 5 = 14 so they give 14 - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.8x + 14
Check. Test with numbers. Put x = 3 into the original and into your answer. The original gives 38 and the answer gives 38. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+4a, +3o, +2a, +5o
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.a terms: +4a, +2a
add the coefficients: 4 + 2 = 6 so they give 6a
o terms: +3o, +5o
add the coefficients: 3 + 5 = 8 so they give 8o - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.6a + 8o
Check. Test with numbers. Put a = 3, o = 4 into the original and into your answer. The original gives 50 and the answer gives 50. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).
Method. Count the rods and the squares separately: rods are lots of x, squares are plain numbers.
- Count the rods. Each rod is one x.3 rods = 3x
- Count the squares. Each square is 1.2 squares = 2
- Write the total. A rod cannot be added to a square, so they stay as two terms.3x + 2
Check. If x were 10 each rod is 10: 3 × 10 + 2 = 32. ✓
Watch out. Do not add 3x + 2 to get 5x.
Method. Substitute numbers into both sides. If the answers differ, the statement is wrong.
- Left side with x = 2, y = 1. 3 × 2 + 4 × 1 = 6 + 4 = 10
- Right side. 7xy means 7 × x × y.7 × 2 × 1 = 14
- Compare. 10 is not 14, so Alex is wrong.
- Explain. x and y are different letters, so 3x and 4y are not like terms. They cannot be added.3x + 4y is already as simple as it can be.
Check. With x = 2, y = 1: 10 ≠ 14. ✓
Watch out. You can only add like terms: the same letters with the same powers.
Method. Think: what must be added to 5x to make 9x?
- Find the difference. The missing term is 9x take away 5x.9x − 5x = 4x
- Write the answer. The missing term is 4x.
Check. 5x + 4x = 9x. ✓
Method. Think: what must be taken away from 7y to leave 2y?
- Find the difference. 7y − 2y = 5y
- Write the answer. The missing term is 5y.
Check. 7y − 5y = 2y. ✓
Method. The missing term must also be an a2 term, because only like terms can combine.
- Find the difference. 8a2 − 3a2 = 5a2
- Write the answer. The missing term is 5a2.
Check. 5a2 + 3a2 = 8a2. ✓
Method. The x terms already match, so the missing term is a y term.
- Compare the y terms. 8y − 3y = 5y
- Write the answer. The missing term is 5y.
Check. 4x + 3y + 5y = 4x + 8y. ✓
Method. Match the like terms on both sides: the x2 terms, the x terms and the numbers must give the answer given.
- Collect the x2 terms. On the left the x2 terms are 3x2 and qx2. Together they must make 7x2.3 + q = 7, so q = 7 − 3 = 4
- Collect the x terms. The x terms are px and −2x. Together they must make 4x.p − 2 = 4, so p = 4 + 2 = 6
- Check the numbers. The plain numbers are 5 and −8, which should make −3.5 − 8 = −3 ✓
Check. Put p = 6, q = 4 back: 3x2 + 6x + 5 + 4x2 − 2x − 8 = 7x2 + 4x − 3. ✓
Watch out. Only match terms of the same kind with each other.
Key words. A term is one part of an expression, together with the sign in front of it (for example 3x or −5). Like terms have exactly the same letters with exactly the same powers (3x and 5x are like terms, 3x and 5x2 are not). The coefficient is the number in front of the letters.
Method. Collect like terms: group the terms that have the same letters and powers, then add or subtract their coefficients (the numbers in front).
- Write the terms out one by one, each with the sign in front of it. A term is one part of the expression. The sign in front of a term belongs to that term, so in 5x − 2y the terms are +5x and −2y. (A term with no sign in front is positive.)+c, +12t, +c, +15t
- Sort the terms into groups of like terms. Like terms have the same letters with the same powers, so they are the same kind of thing. We can only add the same kind of thing: 3 apples + 2 apples = 5 apples, but 3 apples + 2 pears cannot be made into one number. Remember that x and x2 are different kinds of term, and so are x and xy.c terms: +c, +c
add the coefficients: 1 + 1 = 2 so they give 2c
t terms: +12t, +15t
add the coefficients: 12 + 15 = 27 so they give 27t - Write the answer. Join the results of the groups. Put the term with the highest power first, and the number last.2c + 27t
Check. Test with numbers. Put c = 3, t = 4 into the original and into your answer. The original gives 114 and the answer gives 114. They are the same, so the answer is right. ✓ (One test does not prove it, but a wrong answer almost never survives it.)
Watch out. The sign in front of a term goes with it. In 7x − 3x you are taking away 3 lots of x. Also, a letter on its own, such as x, has a coefficient of 1 (and −x has −1).