# How do you multiply (sqrt(6) + 2 sqrt(2))(4sqrt(6) - 3 sqrt(2))?

May 28, 2015

$\left(\textcolor{red}{\sqrt{6}} + \textcolor{b l u e}{2 \sqrt{2}}\right) \times \textcolor{\mathmr{and} a n \ge}{\left(4 \sqrt{6} - 3 \sqrt{2}\right)}$

Distribute the terms of the first factor over the second factor
$= \textcolor{red}{\left(\sqrt{6}\right)} \textcolor{\mathmr{and} a n \ge}{\left(4 \sqrt{6} - 3 \sqrt{2}\right)} + \textcolor{b l u e}{\left(2 \sqrt{2}\right)} \textcolor{\mathmr{and} a n \ge}{\left(4 \sqrt{6} - 3 \sqrt{2}\right)}$

$= \textcolor{red}{\left(4 \left(6\right) - 3 \sqrt{12}\right)} + \textcolor{b l u e}{\left(8 \sqrt{12} - 6 \left(2\right)\right)}$

$= 12 + 5 \sqrt{12}$

$= 12 + 10 \sqrt{3}$