# How do you simplify 2sqrt3(2sqrt3-4sqrt5)?

May 26, 2017

See a solution process below:

#### Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{2 \sqrt{3}} \left(2 \sqrt{3} - 4 \sqrt{5}\right) \implies$

$\left(\textcolor{red}{2 \sqrt{3}} \times 2 \sqrt{3}\right) - \left(\textcolor{red}{2 \sqrt{3}} \times 4 \sqrt{5}\right) \implies$

$\left(\left(2 \times 2\right) \left(\sqrt{3} \times \sqrt{3}\right)\right) - \left(\left(2 \times 4\right) \left(\sqrt{3} \times \sqrt{5}\right)\right) \implies$

$\left(4 \times 3\right) - \left(8 \left(\sqrt{3} \times \sqrt{5}\right)\right) \implies$

$12 - \left(8 \left(\sqrt{3} \times \sqrt{5}\right)\right)$

We can now use this rule of radicals to simplify the term on the right:

$\sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}}$

$12 - \left(8 \left(\sqrt{\textcolor{red}{3}} \times \sqrt{\textcolor{b l u e}{5}}\right)\right) \implies$

$12 - \left(8 \sqrt{\textcolor{red}{3} \times \textcolor{b l u e}{5}}\right) \implies$

$12 - 8 \sqrt{15}$