# Introduction to Distributive Property

The distributive property states that when we multiply a factor and a sum or difference, we multiply the factor by each term of the sum or difference.

### Formula

The distributive property of multiplication for any three real numbers 'a', 'b' and 'c' is
• a × (b + c) = (a × b) + (a × c)

• a × (b − c) = (a × b) − (a × c)

Example

Rewrite 8 × (7 + 4) using distributive property in order to simplify

Solution

Step 1:

According to distributive property for any three real numbers, 'a', 'b' and 'c'

a × (b + c) = (a × b) + (a × c)

Step 2:

8 × (7 + 4) = (8 × 7) + (8 × 4) = 56 + 32 = 88

Rewrite given expression using distributive property in order to simplify

8 × (7 + 4)

### Solution

Step 1:

According to distributive property for any three real numbers, 'a', 'b' and 'c'

a × (b + c) = (a × b) + (a × c)

Step 2:

8 × (7 + 4) = (8 × 7) + (8 × 4) = 56 + 32 = 88

Rewrite given expression using distributive property in order to simplify

9 × (6 − 2)

### Solution

Step 1:

According to distributive property for any three real numbers, 'a', 'b' and 'c'

a × (b − c) = (a × b) − (a × c)

Step 2:

9 × (6 − 2) = (9 × 6) − (9 × 2) = 54 − 18 = 36