Collecting Like Terms On One Side of an Equation

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  • 0:01 Like Terms
  • 1:30 Identifying Like Terms
  • 3:05 Combining Like Terms
  • 4:29 Another Example
  • 5:46 Lesson Summary
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Lesson Transcript
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 are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. Watch this video lesson to see how it is done.

Like Terms

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. But before we can talk about collecting like terms, we need to talk about like terms in general. What are they? Like terms are terms that share the same variable and exponent. You can also say that like terms are terms that like each other. Terms can be a single number, a variable, or a combination of numbers and variables multiplied with each other. If you think of the variable and exponent part of a term as the term's last name, then like terms are those terms that share the same last name and are thus part of the same family. If a term didn't have a variable attached to it, then that means it doesn't have a last name and is, therefore, related to all the other terms without last names, without variables attached. For example, 4x, 7x, and x are all like terms because they all share the same variables with the same exponents. 5x^2, 6x^2, 3x^2 are also all like terms. But, 4x and 3x^2 are not like terms. Why is this? Even though their variables are the same, their exponents are not the same. Yes, for them to be like terms, both the variables and the exponents must match.

Identifying Like Terms

If you saw a group of terms together, you would be able to identify like terms by looking at the variables and exponents of each term. This is the first step of collecting like terms on one side of an equation. Say, for example, we are trying to simplify the equation 4x + 5 + 3x - 2 = 0. If you see a problem asking you to simplify, remember that what it wants is for you to collect like terms together. To do this, we need to first identify which terms are like terms. What I recommend doing is to highlight the various like terms with different colors. I begin by highlighting the 4x. I continue reading my equation to see if there are other terms that are like 4x. I see a 3x with the same variable and exponent. That means that 3x is a like term to 4x. They both share the same last name of x. I keep reading the equation to see if there are more. Nope, that's it. Now I choose a different color highlighter, and I highlight the 5. I keep reading the equation to see if there are more terms that are like 5. Since I've already highlighted some terms, I can concentrate on reading only those terms that haven't been highlighted. Notice how I've included the negative. That negative tells me that the 2 is negative. It's very important to keep the right signs for the next step. I can go on to the next step now that I've highlighted all the terms on the one side of the equation.

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