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

Jul 10, 2015

$- \left(45 \sqrt{3} + 30\right)$

Explanation:

$- 3 \sqrt{5} \left(3 \sqrt{15} + 2 \sqrt{5}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$= \left(- 3 \sqrt{5} \cdot 3 \sqrt{15}\right) + \left(- 3 \sqrt{5} \cdot 2 \sqrt{5}\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= - 9 \sqrt{75} - 6 \sqrt{25}$

$\textcolor{w h i t e}{\text{XXXX}}$$= - 9 \cdot 5 \sqrt{3} - 6 \cdot 5$

$\textcolor{w h i t e}{\text{XXXX}}$$= - \left(45 \sqrt{3} + 30\right)$

Jul 10, 2015

The answer is $- 45 \sqrt{3} - 30$.

Explanation:

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

Distribute the $- 3 \sqrt{5}$ by multiplying it times both terms in the parentheses.

$- 9 \sqrt{5} \sqrt{15} - 6 \sqrt{5} \sqrt{5}$ =

Simplify.

$- 9 \sqrt{5} \sqrt{3} \sqrt{5} - 6 \sqrt{5} \sqrt{5}$ =

Simplify.

$\left(\sqrt{5} \sqrt{5} = 5\right)$

$- 9 \cdot 5 \sqrt{3} - 6 \cdot 5$ =

Simplify.

$- 45 \sqrt{3} - 30$