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: