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Like & Unlike Terms

Instructor: Heather Jenkins

Heather has a bachelor's degree in elementary education and a master's degree in special education. She was a public school teacher and administrator for 11 years.

Did you know numbers can be alike and different? Some can go together while others cannot. In this lesson, you will learn all about like and unlike terms.

What is a Term?

5 + 2

x + y

5x - 3y

What do all these statements have in common? They all contain terms. Wait, what's a term?

A term can be a single number or variable, or a group of numbers and variables. Variables are symbols or letters that stand for an unknown or changing number. For example, x could stand for the number of rubber ducks in your bathtub or how many stinky socks are under your bed...hopefully not a lot!

In the examples above, 5 and 2 are terms that are single numbers. Likewise, x, y, 5x, and 3y are also terms that have variables representing unknown numbers.


Examples of terms
terms


Can We Be Friends?

When you make a new friend, it's usually because you have something in common. Maybe you both enjoy playing soccer or love to make sculptures out of the materials you find in your couch cushions. Gross!

Just like friends have things in common, like terms are terms that have the same variables in common. The variables in the terms are exactly the same including the exponents, or small numbers above the variables. Sometimes numbers may be directly in front of variables. These numbers do not need to be the same. For example, 18y and 19y are still like terms because they share the same variable, y. Numbers without variables are also like terms because they are simply numbers.

The opposite of like terms are unlike terms. Unlike terms are terms that do not have the same variable. Can you figure out which of the following are like terms and which are unlike terms?


Like and unlike terms
terms


The like terms are:

  • Letter A because each term has variables that are exactly alike. Each contains an x with an exponent of 3 and a y with an exponent of 4.
  • Letter D because they are both numbers.

The unlike terms are:

  • Letter B because one term has a variable, x, while the other does not.
  • Letter C because the exponent for one z is 4 and 19 for the other.

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