The Distributive Property Help

The Distributive Property

An important property that is often used in algebra is called the distributive property :

For any numbers a, b, and c, a(b + c) = ab + ac .

The distributive property states that when a sum of two numbers or expressions in parentheses is multiplied by a number outside the parentheses, the same result will occur if you multiply each number or expression inside the parentheses by the number outside the parentheses.

Examples

Example 1

Multiply 5(2x + 3y).

Solution 1

The Distributive Property

Example 2

Multiply 8(x + 3y).

Solution 2

The Distributive Property

The distributive property also works for subtraction.

Example 3

Multiply 9(2x – 4y).

Solution 3

The Distributive Property

The distributive property works for the sum or difference of three or more expressions in parentheses.

Example 4

Multiply 3(6a + 2b – 7c).

Solution 4

The Distributive Property

When a negative number is multiplied, make sure to change the signs of the terms inside the parentheses when multiplying.

Example 5

Multiply –2(6p – 7q – 3r).

Solution 5

The Distributive Property

Math Note: The distributive property is called the distributive property for multiplication over addition.

Practice

Multiply each of the following:

1. 6(3x + 8y)

2. 2(b + 4)

3. 4(7a – 2b + 3c)

4. –3(2p – 5q + 3r)

5. –5(6x – 7y + z)

Answers

1. 18x + 48y

2. 2b + 8

3. 28a – 8b + 12c

4. –6p + 15q – 9r

5. –30x + 35y – 5z

Practice problems for this concept can be found at: Expressions And Equations Practice Test.

The Distributive Property Help