# How do you simplify (7 +3sqrt2)(9- 5sqrt2)?

Jun 1, 2017

See a solution process below:

#### Explanation:

First, we need to multiply the two parenthetical terms. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{7} + \textcolor{red}{3 \sqrt{2}}\right) \left(\textcolor{b l u e}{9} - \textcolor{b l u e}{5 \sqrt{2}}\right)$ becomes:

$\left(\textcolor{red}{7} \times \textcolor{b l u e}{9}\right) - \left(\textcolor{red}{7} \times \textcolor{b l u e}{5 \sqrt{2}}\right) + \left(\textcolor{red}{3 \sqrt{2}} \times \textcolor{b l u e}{9}\right) - \left(\textcolor{red}{3 \sqrt{2}} \times \textcolor{b l u e}{5 \sqrt{2}}\right)$

$63 - 35 \sqrt{2} + 27 \sqrt{2} - 15 {\left(\sqrt{2}\right)}^{2}$

$63 - 35 \sqrt{2} + 27 \sqrt{2} - \left(15 \cdot 2\right)$

$63 - 35 \sqrt{2} + 27 \sqrt{2} - 30$

We can now combine like terms:

$\left(63 - 30\right) + \left(- 35 + 27\right) \sqrt{2}$

$33 + \left(- 8\right) \sqrt{2}$

$33 - 8 \sqrt{2}$