How do you solve  (2+sqrt6)(2-sqrt6)?

1 Answer
Apr 25, 2018

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

Explanation:

As you can see we have two binomials multiplied by each other of the form $\left(a + b\right) \left(a - b\right)$.

There is a useful shortcut for this type of expression:
$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

In this case $a = 2$ and $b = \sqrt{6}$

So

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

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

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