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# Combining Like Terms Lessons

A term is a constant or a variable in an expression. In the equation 12+3x+2x2=5x-1, the terms on the left are 12, 3x and 2x2, while the terms on the right are 5x, and -1.

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.

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