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