**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**

**Example 2**

Multiply 8(x + 3y).

**Solution 2**

The distributive property also works for subtraction.

**Example 3**

Multiply 9(2x – 4y).

**Solution 3**

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**

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**

**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.

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