# How do you simplify -2sqrt15(-3sqrt3+3sqrt5)?

Aug 18, 2017

See a solution process below:

#### Explanation:

First, multiply each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{- 2 \sqrt{15}} \left(- 3 \sqrt{3} + 3 \sqrt{5}\right) \implies$

$\left(\textcolor{red}{- 2 \sqrt{15}} \times - 3 \sqrt{3}\right) + \left(\textcolor{red}{- 2 \sqrt{15}} \times 3 \sqrt{5}\right) \implies$

$\left(\textcolor{red}{- 2} \times - 3\right) \textcolor{red}{\sqrt{15}} \sqrt{3} + \left(\textcolor{red}{- 2} \times 3\right) \textcolor{red}{\sqrt{15}} \sqrt{5} \implies$

$6 \sqrt{15 \times 3} + \left(- 6\right) \sqrt{15 \times 5} \implies$

$6 \sqrt{45} - 6 \sqrt{75}$

Now, we can simplify the radicals:

$6 \sqrt{45} - 6 \sqrt{75} \implies$

$6 \sqrt{9 \times 5} - 6 \sqrt{25 \times 3} \implies$

$6 \sqrt{9} \sqrt{5} - 6 \sqrt{25} \sqrt{3} \implies$

$\left(6 \cdot 3\right) \sqrt{5} - \left(6 \cdot 5\right) \sqrt{3} \implies$

$18 \sqrt{5} - 30 \sqrt{3}$

Aug 18, 2017

$18 \sqrt{5} - 30 \sqrt{3}$

#### Explanation:

First, distribute the $- 2 \sqrt{15}$
You end up with:
$6 \sqrt{45} - 6 \sqrt{75}$
You can then factor under the radical.
$6 \sqrt{9 \cdot 5} - 6 \sqrt{25 \cdot 5}$
Then, simplify by square rooting the perfect squares.
$6 \cdot 3 \sqrt{5} - 6 \cdot 5 \sqrt{3}$
Then multiply.
$18 \sqrt{5} - 30 \sqrt{3}$