# How do you simplify (3 sqrt(2) + 2 sqrt(5))(4 sqrt(2) - sqrt(5))?

$\frac{34 + 11 \sqrt{10}}{27}$
$\frac{3 \sqrt{2} + 2 \sqrt{5}}{4 \sqrt{2} - \sqrt{5}} \cdot \frac{4 \sqrt{2} + \sqrt{5}}{4 \sqrt{2} + \sqrt{5}}$
$= \frac{24 + 3 \sqrt{10} + 8 \sqrt{10} + 10}{32 - 5}$
$= \frac{34 + 11 \sqrt{10}}{27}$