# How do you simplify (2- sqrt 2) (2 + sqrt2)?

Jun 10, 2016

$\left(2 - \sqrt{2}\right) \left(2 + \sqrt{2}\right) = \textcolor{g r e e n}{2}$

#### Explanation:

Remember the general equation for the difference of squares:
$\textcolor{w h i t e}{\text{XXX}} \left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$

Given $\left(2 - \sqrt{2}\right) \left(2 + \sqrt{2}\right)$
we can treat $a$ as $2$
and $b$ as $\sqrt{2}$

So
$\textcolor{w h i t e}{\text{XXX}} \left(2 - \sqrt{2}\right) \left(2 + \sqrt{2}\right)$
$\textcolor{w h i t e}{\text{XXXXX}} = \left({2}^{2} - {\left(\sqrt{2}\right)}^{2}\right)$
$\textcolor{w h i t e}{\text{XXXXX}} = 4 - 2$
$\textcolor{w h i t e}{\text{XXXXX}} = 2$