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The Distributive Property

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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.

  1. Parenthesis
  2. Exponents
  3. Multiplication or Division
  4. Addition or Subtraction

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

5(8-2)

  1. 5(6)
  2. 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)

  1. 14*3 +14*x
  2. 42 + 14x 

Be careful, 42 + 14x is not 56x.

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