The Distributive Property is useful because of the unknown nature of Algebra. Back in the good old days (elementary school), this type of problem would be presented:

Simplify 5(8-2).

Order of Operations dictates the sequence of completing mathematical operations.

- Parenthesis
- Exponents
- Multiplication or Division
- Addition or Subtraction

To simplify 5(8-2), use the following steps:

5(8-2)

- 5(6)
- 5*6 = 30

### Distributive Property Example

What if the exercise looked like this?

Simplify 14(3 +

x).

Nothing can be done inside of the parenthesis because 3 and *x* can't be combined. Don’t dismay, the distributive property is here to save the day!

Illustration of the Distributive Property

a(b+c) =ab+ac

In other words,

14(3 +

x)

- 14*3 +14*
*x* - 42 + 14
*x*

Be careful, 42 + 14*x* is not 56*x*.