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

May 7, 2018

$\left(x + 2\right) \left(x - 2\right) = {x}^{2} - 4$

#### Explanation:

Use the distributive property to multiply both terms in the first set of parenthesis by the terms in the second set:
First the $x$:
$x \cdot x = {x}^{2}$.
$x \cdot \left(- 2\right) = - 2 x$.
Now the $2$:
$2 \cdot x = 2 x$.
$2 \cdot \left(- 2\right) = - 4$.
We came up with four terms: ${x}^{2} - 2 x + 2 x - 4$.
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