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Combining Like Terms

In an Expression

Consider the expression below:

5x2 + 7x + 2 - 2x2 + 7 + x2

We will demonstrate how to simplify this expression by combining like terms. First, we identify sets of like terms. Both 2 and 7 are like terms because they are both constants. The terms 5x2, -2x2, and x2 are like terms because they each consist of a constant times x squared.

Now the coefficients of each set of like terms are added. The coefficients of the first set are the constants themselves, 2 and 7. When added the result is 9. The coefficients of the second set of like terms are 5, -2, and 1. Therefore, when added the result is 4.

With the like terms combined, the expression becomes

9 + 7x + 4x2

The Combining Like Terms process is also used to make equations easier to solve.

While Solving an Equation

The equation which we will be simplifying and solving is below.

x + 3x + 7 = 42 + x - 12

When combining like terms it is important to preserve the equality of the equation by only combining like terms on one side at a time. We will simplify the left hand side first. The first step is to find pairs of like terms, the second step is to add. The x and 3x are like terms, so they are added resulting in 4x. (HINT: when a variable such as x has no coefficient, its coefficient is 1 so x is the same as 1x.) The 7 does not have a like term, so it is not changed. The equation now reads

4x + 7 = 42 + x - 12

The next step is to simplify the right hand side of the equation. This time there is no term which can be added with x, but there are two constants which are like terms. The 42 and the -12 are added, resulting in 30. The equation now reads.

4x + 7 = x + 30

The equation is now similar to those presented in the Equation Basics lesson, therefore the solution can be completed using the methods learned there.

Another example is presented on the next page.

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