# How do you simplify  (sqrt2 + sqrt6)(sqrt2 - sqrt6)?

Jun 2, 2016

The result is -4.

#### Explanation:

When you multiply two numbers in the form $\left(A + B\right) \left(A - B\right)$ you obtain as result ${A}^{2} - {B}^{2}$.

In your case $A = \sqrt{2}$ and $B = \sqrt{6}$ then

$\left(\sqrt{2} + \sqrt{6}\right) \left(\sqrt{2} - \sqrt{6}\right) = {\sqrt{2}}^{2} - {\sqrt{6}}^{2} = 2 - 6 = - 4$.

Jun 2, 2016

$2 - 6 = - 4$

#### Explanation:

This is in the same format as $\left(x + y\right) \left(x - y\right)$ which are the factors of ${x}^{2} - {y}^{2} , \text{ known as the difference between two squares}$

So if $\left(x + y\right) \left(x - y\right) = {x}^{2} - {y}^{2}$, then

$\left(\sqrt{2} + \sqrt{6}\right) \left(\sqrt{2} - \sqrt{6}\right) = {\left(\sqrt{2}\right)}^{2} - {\left(\sqrt{6}\right)}^{2}$

This simplifies to $2 - 6 = - 4$

This could also be simplified by multiplying out the brackets to get 4 terms, but the answer will be the same - it will just take longer.