# How do you multiply (3sqrt2 - 9)(3sqrt2 +9)?

Jun 13, 2015

This is of the form $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$, so

$\left(3 \sqrt{2} - 9\right) \left(3 \sqrt{2} + 9\right) = {\left(3 \sqrt{2}\right)}^{2} - {9}^{2} = 18 - 81 = - 63$

#### Explanation:

Standard difference of squares identity.

$\left(3 \sqrt{2} - 9\right) \left(3 \sqrt{2} + 9\right)$

$= {\left(3 \sqrt{2}\right)}^{2} - {9}^{2}$

$= \left({3}^{2} {\sqrt{2}}^{2}\right) - {9}^{2}$

$= \left(9 \cdot 2\right) - 81 = 18 - 81 = - 63$