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

Apr 5, 2017

${x}^{2} - 4$

#### Explanation:

law of multiplying brackets:
$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

using this:

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

$= {x}^{2} - 4$

Apr 5, 2017

See the entire solution process below:

#### Explanation:

This is a special form which follows this rule:

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

Substituting $x$ for $a$ and $2$ for $b$ gives:

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

We can also do the long form of this multiplication. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{x} + \textcolor{red}{2}\right) \left(\textcolor{b l u e}{x} - \textcolor{b l u e}{2}\right)$ becomes:

$\left(\textcolor{red}{x} \times \textcolor{b l u e}{x}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{2}\right) + \left(\textcolor{red}{2} \times \textcolor{b l u e}{x}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{2}\right)$

${x}^{2} - 2 x + 2 x - 4$

We can now combine like terms:

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

${x}^{2} + \left(0\right) x - 4$

${x}^{2} + 0 - 4$

${x}^{2} - 4$