How do you simplify #(x + 2)(x - 2)#?

1 Answer
May 7, 2018

Answer:

#(x+2)(x-2)=x^2-4#

Explanation:

Use the distributive property to multiply both terms in the first set of parenthesis by the terms in the second set:
First the #x#:
#x*x=x^2#.
#x*(-2)=-2x#.
Now the #2#:
#2*x=2x#.
#2*(-2)=-4#.
We came up with four terms: #x^2-2x+2x-4#.
Simplify the expression by adding the middle terms, and we get just #x^2-4#.

This is a special kind of binomial (a binomial is an expression with two terms) called a difference of squares. Since #(x+2)&(x-2)# are the same except for the sign in between, the answer is just the first term squared (#x^2#) minus the second term squared
-(#2^2)=-4#.
Here's more about difference of squares: https://www.mathsisfun.com/definitions/difference-of-squares.html