Combining Like Terms: Definition, Simplifying & Practice

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  • 0:05 What Are Like Terms?
  • 1:02 Combining Like Terms
  • 2:01 Practice
  • 3:36 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
Combining like terms is a mathematical process used to simplify an expression or to add or subtract polynomials. Learn how to recognize like terms and combine them in this lesson, then check your knowledge with a quiz.

What Are Like Terms?

A term is a mathematical item in an equation that can be a constant (only a number) or a variable (a combination of numbers and letters that possibly have exponents). The number portion of a variable is called the coefficient. Some examples of terms include:

  • 3 (a constant)
  • 2x (a variable)
  • 5y^2 (a variable)
  • 3x2y^3 (a variable)

Like terms are terms that have the same variables and exponents. They do not have to have to be the same coefficients.

Combining Like Terms

When you were first learning to add, the problems you solved might have looked something like this: 'Tim has three apples, and Jane has two apples. Together, how many apples do they have?'

As the problems got more complicated, they might have looked something like this: 'Tim has three apples and four oranges. Jane has two apples and six oranges. If they put all their fruit in one basket, how many apples and oranges do Tim and Jane have?'

When you solve this problem, you can't just randomly add things together without respect to their type. You also can't add them all together and then combine the word - like they have 15 'orpples' or 'appnges.' You have to add the apples (there are five total) and the oranges (ten total) separately in order to solve the problem correctly.

Combining like terms is just like the problem with the apples and oranges. You can only add (or subtract) terms that are the same. And you don't combine variables; they will not change.

Practice

Let's try combining some like terms.

Simplify: x + 4x

These terms are like terms because they both only contain the variable x so they can be combined. If there isn't a number in front of the variable, it's understood to be 1.

1x + 4x = 5x

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