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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.

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 3(x + 5) = 3x + 15. We can also use the distributive property in the other direction and factor an expression, for example 8x + 12 = 4(2x + 3).

We can organize the work of using distributive property to rewrite the expression 12x - 8. In this case we know the product and need to find the factors.

The terms of the product go inside:

Find the value of each expression mentally.

2 + 3 • 4

(2 + 3)(4)

2 - 3 • 4

2 - (3 + 4)

*To write an equivalent expression by factoring means to use the distributive property to write a sum as a product. *

*To write an equivalent expression by expanding means to use the distributive property to write a product as a sum.*

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.

*Hint* for Row #5 -(2x - 3y) = -1 • (2x - 3y)

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