# Distributive Property

## Definition of Distributive Property

Distributive Property states that the product of a number and a sum is equal to the sum of the individual products of the addends and the number.

That is, *a(b + c) = ab + ac
a(b + c) = ab + ac is known as left distributive
(b + c)a = ba + ca is known as right distributive*

### More About Distributive Property

The property is true for any number of addends.

That is,* a(b + c + d + . . . .) = ab + ac + ad + . . . . . *

Also,

*a(b - c) = ab - ac and
a (b - c - d - . . . ) = ab - ac - ad - . . . *

### Example of Distributive Property

5(3 + 1) = 5 x 3 + 5 x 1

Consider LHS: 5(3 + 1) = 5(4) = 20

Consider RHS: 5 x 3 + 5 x 1 = 15 + 5 = 20

LHS = RHS

### Video Examples: The Distributive Property

### Solved Example on Distributive Property

**Ques: **Using the distributive property, evaluate x(y + 2), for x = 2 and y = 5.

##### Choices:

- A. 14
- B. 12
- C. 20
- D. 9

Correct Answer: A

### Solution:

- Step 1: x(y + 2) = xy + 2x, using the distributive property
- Step 2: Substitute the values of x and y in the expression
- Step 3: = 2 x 5 + 2 x 2 = 10 + 4 = 14