Lesson 19Expanding and Factoring
Learning Goal
Let’s use the distributive property to write expressions in different ways.
Learning Targets
I can organize my work when I use the distributive property.
I can use the distributive property to rewrite expressions with positive and negative numbers.
I understand that factoring and expanding are words used to describe using the distributive property to write equivalent expressions.
Lesson Terms
- factor (an expression)
- term
Warm Up: Number Talk: Parentheses
Problem 1
Find the value of each expression mentally.
Activity 1: Factoring and Expanding with Negative Numbers
Problem 1
In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.
factored | expanded |
---|---|
Are you ready for more?
Problem 1
Expand to create an equivalent expression that uses the fewest number of terms:
Lesson Summary
We can use properties of operations in different ways to rewrite expressions and create equivalent expressions. We have already seen that we can use the distributive property to expand an expression, for example
We can organize the work of using distributive property to rewrite the expression
The terms of the product go inside:
We look at the expressions and think about a factor they have in common.
Now we think: “
So,