# How do you simplify (5 + 2sqrt2)(8 - 3sqrt2)?

Jul 19, 2018

See a solution process below:

#### Explanation:

To multiply and simplify these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{5} + \textcolor{red}{2 \sqrt{2}}\right) \left(\textcolor{b l u e}{8} - \textcolor{b l u e}{3 \sqrt{2}}\right)$ becomes:

$\left(\textcolor{red}{5} \times \textcolor{b l u e}{8}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{3 \sqrt{2}}\right) + \left(\textcolor{red}{2 \sqrt{2}} \times \textcolor{b l u e}{8}\right) - \left(\textcolor{red}{2 \sqrt{2}} \times \textcolor{b l u e}{3 \sqrt{2}}\right)$

$40 - 15 \sqrt{2} + 16 \sqrt{2} - 6 {\left(\sqrt{2}\right)}^{2}$

$40 + \left(- 15 + 16\right) \sqrt{2} - \left(6 \times 2\right)$

$40 + 1 \sqrt{2} - 12$

$40 + \sqrt{2} - 12$

$40 - 12 + \sqrt{2}$

$28 + \sqrt{2}$