Simplify Expressions Using the Distributive Property: Mini-Lesson Review

Mini Lesson Question

Question #2: Simplify Expressions Using the Distributive Property

Which expression is equivalent to

-2(x-4)

$2x-8$
$-2x+8$
$-2x-8$
$-2x-4$

Simplify Expressions Using the Distributive Property

The Distributive Property can be used to remove parentheses as you simplify expressions.

DISTRIBUTIVE PROPERTY

$\begin{matrix} If a, b, c are real numbers, then & a (b + c) = a b + a c \\ Also, & (b + c) a = b a + c a \\ a (b - c) = a b - a c \\ (b - c) a = b a - c a \end{matrix}$

Simplify:

1. $3 (x + 4)$

It may help to use arrows to show the Distributive Property.

Use the Distributive Property.

$3 \cdot x + 3 \cdot 4$

Multiply.

$3 x + 12$

2. $- 11 (4 - 3 a)$

Use arrows to show the Distributive Property.

Use the Distributive Property

$- 11 \cdot 4 - (- 11) \cdot 3 a$

Multiply.

$- 44 - (- 33 a)$

Simplify.

$- 44 + 33 a$

Watch signs when using the Distributive Property with negative signs.

Try it

Simplify Expressions Using the Distributive Property

Simplify: $- 2 (4 y + 1)$ .

Here is how to simplify expressions using the Distributive Property.

Use arrows to show the Distributive Property.

Use the Distributive Property.

$- 2 \cdot 4 y + (- 2) \cdot 1$

Multiply.

$- 8 y + (- 2)$

Simplify.

$- 8 y - 2$

Check Your Understanding

Which expression is equivalent to $4 (5 - 2 a)$ ?

$20 - 2 a$
$20 + 2 a$
$20 - 8 a$
$20 + 8 a$

$20 - 8 a$

Check yourself: When using the Distributive Property, the factor outside of the parentheses is multiplied by each term inside the parentheses. So, 4(5) and 4(-2a) results in 20 - 8a.

Videos: Using the Distributive Property to Simplify Expressions

Watch the first 2 minutes and 40 seconds of the video to see how to use the Distributive Property to simplify expressions.

Khan Academy: Distributive property with variables

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