Lesson 22

Combining Like Terms (Part 3)

Let’s see how we can combine terms in an expression to write it with less terms.

22.1: Are They Equal?

Select all expressions that are equal to .

22.2: X’s and Y’s

Match each expression in column A with an equivalent expression from column B. Be prepared to explain your reasoning.

A

B

 

22.3: Seeing Structure and Factoring

Write each expression with fewer terms. Show or explain your reasoning.

Summary

Combining like terms is a useful strategy that we will see again and again in our future work with mathematical expressions. It is helpful to review the things we have learned about this important concept.

  • Combining like terms is an application of the distributive property. For example:

  • It often also involves the commutative and associative properties to change the order or grouping of addition. For example:

  • We can't change order or grouping when subtracting; so in order to apply the commutative or associative properties to expressions with subtraction, we need to rewrite subtraction as addition. For example:

  • Since combining like terms uses properties of operations, it results in expressions that are equivalent.

  • The like terms that are combined do not have to be a single number or variable; they may be longer expressions as well. Terms can be combined in any sum where there is a common factor in all the terms. For example, each term in the expression has a factor of . We can rewrite the expression with fewer terms by using the distributive property: 

Video Summary

Glossary Entries

  • expand

    To expand an expression, we use the distributive property to rewrite a product as a sum. The new expression is equivalent to the original expression.

    For example, we can expand the expression to get the equivalent expression .

  • factor (an expression)

    To factor an expression, we use the distributive property to rewrite a sum as a product. The new expression is equivalent to the original expression.

    For example, we can factor the expression to get the equivalent expression .

  • term

    A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together. For example, the expression has two terms. The first term is and the second term is 18.