Lesson 22Combining Like Terms (Part 3)

Learning Goal

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

Learning Targets

  • Given an expression, I can use various strategies to write an equivalent expression.

  • When I look at an expression, I can notice if some parts have common factors and make the expression shorter by combining those parts.

Lesson Terms

  • expand
  • factor
  • factor (an expression)
  • term

Warm Up: Are They Equal?

Problem 1

Select all expressions that are equal to .

Activity 1: X’s and Y’s

Problem 1

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

A

B

Activity 2: Seeing Structure and Factoring

Problem 1

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

Lesson 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: