Like terms are terms that are similar. To be like terms, the variables (letters) and their exponents must all be the same. If terms are alike they can be added and subtracted.

 

Example

 

Simplify 3x + 2 + 5

The only like terms in this expression are the 2 and 5. Go ahead and add them to get 7.

 

3x + 7

 

Answer! There are no more like terms that can be combined.

 

 

 

Example

 

Simplify 3x + 2y + 5x + 4 – 7

 

In this example there are two kinds of like terms, the x’s (3x and 5x), and the constants (4 and – 7). Go ahead and combine them. 3x + 5x = 8x and 4 – 7 = –3.

 

8x + 2y – 3

 

There are no more like terms so this is all that can be done.

 

Note- When writing an expression or equation, write the terms with letters in alphabetical order first and then the number term last (constant). That is why the x’s came first and then the y’s in the previous example.

 

 

 

Example

Simplify 3a + 2b + 5y + 4b + a - 7b

 

Note- The fifth term (a) is understood to have a 1 in front of it. Since nothing changes when it is multiplied it by 1, it may be easier to understand it as 1a.

 

3a + 2b + 5y + 4b + 1a - 7b

 

The like terms are the a’s (3a and 1a) and b’s (2b, 4b, and –7b). Combine the like terms.

4a – 1b + 5y

 

Simplify

 

4a – b + 5y

 

Answer!

 

If the variables have exponents, then all the exponents have to be the same to have like terms.

 

If the problem involves square roots then the numbers and variables underneath the radical must also be the same to have like terms.