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

Jul 6, 2016

$12 + 7 \sqrt{6}$

#### Explanation:

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

Each term in the first bracket has to be multiplied by each term in the other bracket.

Note: $\sqrt{3} \times \sqrt{3} = {\sqrt{3}}^{2} = 3$

$\left(6 \sqrt{3} \times \sqrt{3}\right) - \left(2 \sqrt{3} \times \sqrt{2}\right) + \left(9 \sqrt{2} \sqrt{3}\right) - \left(3 \sqrt{2} \times \sqrt{2}\right)$

$6 \times 3 + \left(- 2 \sqrt{6} + 9 \sqrt{6}\right) - 3 \times 2$

$18 + 7 \sqrt{6} - 6$

$12 + 7 \sqrt{6}$