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