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# Combination of Like Terms Help

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By McGraw-Hill Professional
Updated on Sep 26, 2011

## Combining Like Terms

Two or more terms are alike if they have the same variables and the exponents (or roots) on those variables are the same: 3 x 2 y and 5 x 2 y are like terms but 6 xy and 4 xy 2 are not. Constants are terms with no variables. The number in front of the variable(s) is the coefficient —in 4 x 2 y 3 , 4 is the coefficient. If no number appears in front of the variable, then the coefficient is 1. Add or subtract like terms by adding or subtracting their coefficients.

#### Examples

3 x 2 + 4 xy – 8 xy 2 – (2 x 2 – 3 xy – 4 xy 2 + 6) = 3 x 2 + 4 xy – 8 xy 2 – 2 x 2 + 3 xy + 4 xy 2 – 6

= 3 x 2 – 2 x 2 – 8 xy 2 + 4 xy 2 + 4 xy + 3 xy – 6

= (3 – 2) x 2 + (–8 + 4) xy 2 + (4 + 3) xy – 6

= x 2 – 4 xy 2 + 7 xy – 6

## Combining Like Terms Practice Problems

#### Practice

1. 3 xy + 7 xy =

2. 4 x 2 – 6 x 2 =

5. 2 xy 2 – 4 x 2 y – 7 xy 2 + 17 x 2 y =

6. 14 x + 8 – (2 x – 4) =

7. 16 x –4 + 3 x –2 – 4 x + 9 x –4x –2 + 5 x – 6 =

9. x 2 y + xy 2 + 6 x + 4 – (4 x 2 y + 3 xy 2 – 2 x + 5) =

#### Solutions

1. 3 xy + 7 xy = (3 + 7) xy = 10 xy

2. 4 x 2 – 6 x 2 = (4 – 6) x 2 = –2 x 2

5. 2 xy 2 – 4 x 2 y – 7 xy 2 + 17 x 2 y = 2 xy 2 – 7 xy 2 – 4 x 2 y + 17 x 2 y

= (2 – 7) xy 2 +(–4 + 17) x 2 y

= –5 xy 2 + 13 x 2 y

6. 14 x + 8 – (2 x – 4) = 14 x + 8 – 2 x + 4 = 14 x – 2 x + 8 + 4

= (14 – 2) x + 12 = 12 x + 12

7. 16 x –4 + 3 x –2 – 4 x + 9 x –4x –2 + 5 x – 6

= 16 x –4 + 9 x –4 + 3 x –2x –2 – 4 x + 5 x – 6

= (16 + 9) x –4 +(3 – 1) x –2 +(–4 + 5) x – 6

= 25 x –4 + 2 x –2 + x – 6

9. x 2 y + xy 2 + 6 x + 4 – (4 x 2 y + 3 xy 2 – 2 x + 5)

= x 2 y + xy 2 + 6 x + 4 – 4 x 2 y – 3 xy 2 + 2 x – 5

= x 2 y – 4 x 2 y + xy 2 – 3 xy 2 + 6 x + 2 x + 4 – 5

= (1 – 4) x 2 y +(1 – 3) xy 2 + (6 + 2) x – 1

= –3 x 2 y – 2 xy 2 + 8 x – 1

Practice problems for this concept can be found at: Algebra Factoring Practice Test.

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