# How do you simplify (3sqrt3 - 4sqrt2)(2sqrt3 + 4sqrt2)?

Sep 10, 2016

$= 4 \sqrt{6} - 14$

#### Explanation:

Recall: $\sqrt{x} \times \sqrt{x} = \sqrt{{x}^{2}} = {\left(\sqrt{x}\right)}^{2} = x$

and $\sqrt{x} \times \sqrt{y} = \sqrt{x y}$

Each term in the first bracket must be multiplied by each term in the second bracket. This will give 4 terms, which might simplify.

$\left(3 \sqrt{3} - 4 \sqrt{2}\right) \left(2 \sqrt{3} + 4 \sqrt{2}\right)$

=$6 \times 3 + 12 \sqrt{6} - 8 \sqrt{6} - 16 \times 2$

=$18 + 4 \sqrt{6} - 32$

$= 4 \sqrt{6} - 14$