# How do you simplify (5+sqrt3)(4-2sqrt 3)?

Sep 15, 2016

$\left(5 + \sqrt{3}\right) \left(4 - 2 \sqrt{3}\right) = 14 - 6 \sqrt{3}$

#### Explanation:

$\left(5 + \sqrt{3}\right) \left(4 - 2 \sqrt{3}\right)$

= $5 \left(4 - 2 \sqrt{3}\right) + \sqrt{3} \left(4 - 2 \sqrt{3}\right)$

= $20 - 5 \times 2 \sqrt{3} + \sqrt{3} \times 4 - \sqrt{3} \times 2 \sqrt{3}$

= $20 - 10 \sqrt{3} + 4 \sqrt{3} - 2 \times {\left(\sqrt{3}\right)}^{2}$

= $20 - 6 \sqrt{3} - 2 \times 3$

= $20 - - 6 \sqrt{3} - 6$

= $14 - 6 \sqrt{3}$