Combining Like Terms

Combining Like Terms is a process used to simplify an expression or an equation using addition and subtraction of the coefficients of terms. Consider the expression below

5 + 7

By adding 5 and 7, you can easily find that the expression is equivalent to

12

What Does Combining Like Terms Do?

Algebraic expressions can be simplified like the example above by Combining Like Terms. Consider the algebraic expression below:

12x + 7 + 5x

As you will soon learn, 12x and 5x are like terms. Therefore the coefficients, 12 and 5, can be added. This is a simple example of Combining Like Terms.

17x + 7

What are Like Terms?

The key to using and understanding the method of Combining Like Terms is to understand like terms and be able to identify when a pair of terms is a pair of like terms. Some examples of like terms are presented below.

The following are like terms because each term consists of a single variable, x, and a numeric coefficient.

2x, 45x, x, 0x, -26x, -x

Each of the following are like terms because they are all constants.

15, -2, 27, 9043, 0.6

Each of the following are like terms because they are all y² with a coefficient.

3y2, y2, -y2, 26y2

For comparison, below are a few examples of unlike terms.

The following two terms both have a single variable with an exponent of 1, but the terms are not alike since different variables are used.

17x, 17z

Each y variable in the terms below has a different exponent, therefore these are unlike terms.

15y, 19y2, 31y5

Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either.

19x, 14xy

The next page will walk you through the process of combining like terms in a simple equation.