# How would you simplify (2 sqrt 7 - 4 sqrt3)(4 sqrt 7 + 8 sqrt3)?

Feb 18, 2016

-40

#### Explanation:

$\left(2 \sqrt{7} - 4 \sqrt{3}\right) \left(4 \sqrt{7} + 8 \sqrt{3}\right)$

You have to use the distributive operation of multiplication:

$2 \sqrt{7} \times 4 \sqrt{7} + 2 \sqrt{7} \times 8 \sqrt{3} - 4 \sqrt{3} \times 4 \sqrt{7} - 4 \sqrt{3} \times 8 \sqrt{3}$

=$2 \times 4 \times 7 + 2 \times 8 \times \sqrt{7} \times \sqrt{3} - 4 \times 4 \times \sqrt{3} \times \sqrt{7} - 4 \times 8 \times 3$

=$56 + 16 \sqrt{21} - 16 \sqrt{21} - 96 = - 40$