Expanding expressions

Concept

Some expressions use parentheses to show multiplication. When you expand an expression, you get rid of those parentheses. You can use the distributive property to expand expressions. Multiply the term outside the parentheses by each term inside the parentheses. Then add those products.

Rules

1. Use the distributive property to expand the expression.
a(b + c) = a x b + a x c
2. Simplify the expression

Example

Use the distributive property to solve.
-2(5x + 4y)

Solution

-2(5x + 4y)
1. Use the distributive property to expand the expression.
a(b + c) = a x b + a x c
-2(5x + 4y)
-2(5x) + (-2)(4y)

2. Simplify the expression
-2(5x) + (-2)(4y)
-10x – 8y

Practice Expanding Expressions

Practice Problem 1

Drag the numbers to expand the expression using the distributive property.

Practice Problem 2

Select the expression that is equivalent.
$\fn_phv 5.2\times (-\frac{7}{8})-5.2\times8$

Practice Problem 3

Michael had $25 in his wallet. He spent $12.75 on the taxi, and his Grandpa gave him 3 times what he now has in his wallet.
Write an expression using the distributive property to represent the total amount. Then simplify the expression to find how much money Michael has in his wallet.

Distributive Property – to multiply a sum or difference by a number, multiply each term inside the parentheses by the number outside the parentheses.

Pre-requisite Skill
Multiplying Using Basic Facts and Patterns