How do you simplify (3sqrt2+sqrt5)(sqrt2-3sqrt(5r))?

Jun 13, 2018

$6 - 9 \sqrt{10 r} + \sqrt{10} - 15 \sqrt{r}$

Explanation:

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

To simplify this, we will use the distributive method called FOIL:

Following this image, we can multiply it out.

The $\textcolor{t e a l}{\text{firsts}}$:
$\textcolor{t e a l}{3 \sqrt{2} \cdot \sqrt{2}} = 3 \sqrt{4} = 3 \cdot 2 = 6$

The $\textcolor{\in \mathrm{di} g o}{\text{outers}}$:
$\textcolor{\in \mathrm{di} g o}{3 \sqrt{2} \cdot - 3 \sqrt{5 r}} = 3 \cdot - 3 \cdot \sqrt{2 \cdot 5 r} = - 9 \sqrt{10 r}$

The $\textcolor{p e r u}{\text{inners}}$:
$\textcolor{p e r u}{\sqrt{5} \cdot \sqrt{2}} = \sqrt{5 \cdot 2} = \sqrt{10}$

The $\textcolor{o l i v e \mathrm{dr} a b}{\text{lasts}}$:
$\textcolor{o l i v e \mathrm{dr} a b}{\sqrt{5} \cdot - 3 \sqrt{5 r}} = - 3 \sqrt{5 \cdot 5 r} = - 3 \sqrt{25 r} = - 3 \cdot 5 \sqrt{r} = - 15 \sqrt{r}$

$6 - 9 \sqrt{10 r} + \sqrt{10} - 15 \sqrt{r}$