Combining Like Terms with the Distributive Property

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When you have terms in parentheses in your problem, you have to be careful that you always evaluate these terms first before trying to combine like terms. If you don't, you'll get a wrong answer. Learn how to do this in this lesson.

Combining Like Terms

When you get to algebra, you begin to work with problems such as these:

like terms distributive property

You'll be given these types of problems and you'll be asked to combine your like terms. Remember, like terms are the terms that have a number multiplied by the same variable. So 4x and 2x are like terms as are 3y and 5y. But 4x and 3y are not like terms, nor are 4x and 4y. This is because they do not share the same variable. For two terms to be like terms, all the variables in the term must be the same. For example, if you had an x2 term, another like term must also have x2 for the variable part. If it had anything else, even if it was an x, it would not be a like term. Terms are separated by addition, subtraction, or division.

Combining your like terms is not difficult in itself. It comes down to simply adding or subtracting as needed. But when you also have parentheses to worry about, and possibly the distributive property to apply, then combining your like terms gets a little bit trickier. When you have a a term next to a pair of parentheses, the distributive property tells you to multiply that term with all the other terms inside the parentheses.

Don't worry, follow these steps and you'll be okay.

Step 1: Apply the distributive property wherever you have parentheses.

The first step you need to do is to apply the distributive property. Once you have applied the distributive property, your parentheses will go away.

Looking at the problem 4x + x ( 3 - 2y ), you see a pair of parentheses with an x term in front of it. This means you need to apply the distributive property and multiply the x with all the terms inside the parentheses. Doing that you get this.

like terms distributive property

Now, you don't have any parentheses left.

Step 2: Combine your terms.

Now that you've taken care of your parentheses, you can now go ahead and combine your like terms. Remember, only add or subtract those terms that have exactly the same number and type of variable.

For your problem, 4x + 3x - 2xy, the only terms that are like terms are 4x and 3x. The -2xy is not a like term to any of the others. So you go ahead and add your 4x and 3x together to get 7x.

  • 4x + 3x = 7x

The Solution

Your answer then is 7x - 2xy. You have combined all the like terms that you could and you are done.

  • 7x - 2xy

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