# How do you simplify (4sqrt5 + sqrt3)(2sqrt2 - sqrt7)?

Jan 23, 2016

$8 \sqrt{10} - 4 \sqrt{35} + 2 \sqrt{6} - \sqrt{21}$

#### Explanation:

Note that $\sqrt{a} \left(\sqrt{b}\right) = \sqrt{a b}$ if $a , b \ge 0$.

To simplify this, we can distribute using the foil method.

${\overbrace{4 \sqrt{5} \left(2 \sqrt{2}\right)}}^{\text{First"+overbrace(4sqrt5(-sqrt7))^"Outside"+overbrace(sqrt3(2sqrt2))^"Inside"+overbrace(sqrt3(-sqrt7))^"Last}}$

Which, using the first rule, yields

$8 \sqrt{10} - 4 \sqrt{35} + 2 \sqrt{6} - \sqrt{21}$