What is (5+square root of 3)(4-2square root of 3)?

Jul 30, 2018

$14 - 6 \sqrt{3}$

Explanation:

We use the FOIL method to multiply these two expressions.

This means first multiply the terms which occur first in each expression i.e. $5$ and $4$.
Next, we multiply the innermost terms i.e. $\sqrt{3}$ and $4$.
Then, we multiply the outermost terms i.e. $5$ and $- 2 \sqrt{3}$.
Finally, we multiply the terms that occur last in each expression i.e. $\sqrt{3}$ and $- 2 \sqrt{3}$, and add them all up.

$\left(5 + \sqrt{3}\right) \left(4 - 2 \sqrt{3}\right)$
$= 20 + 4 \sqrt{3} - 10 \sqrt{3} - 6$
$= 14 - 6 \sqrt{3}$