# How do you simplify (4+3sqrt3) (9-2sqrt3)?

Jul 9, 2017

It needs plain multiplication.

#### Explanation:

$\left(4 + 3 \sqrt{3}\right) \left(9 - 2 \sqrt{3}\right)$
=(4×9)-(4×2sqrt3)+(9×3sqrt3)-(3sqrt3×2sqrt3)
$= 18 + 19 \sqrt{3}$

Jul 9, 2017

See a solution process below:

#### Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{4} + \textcolor{red}{3 \sqrt{3}}\right) \left(\textcolor{b l u e}{9} - \textcolor{b l u e}{2 \sqrt{3}}\right)$ becomes:

$\left(\textcolor{red}{4} \times \textcolor{b l u e}{9}\right) - \left(\textcolor{red}{4} \times \textcolor{b l u e}{2 \sqrt{3}}\right) + \left(\textcolor{red}{3 \sqrt{3}} \times \textcolor{b l u e}{9}\right) - \left(\textcolor{red}{3 \sqrt{3}} \times \textcolor{b l u e}{2 \sqrt{3}}\right)$

$36 - 8 \sqrt{3} + 27 \sqrt{3} - 6 \left(\sqrt{3} \sqrt{3}\right)$

$36 - 8 \sqrt{3} + 27 \sqrt{3} - \left(6 \cdot 3\right)$

$36 - 8 \sqrt{3} + 27 \sqrt{3} - 18$

Now, we can group and combine like terms:

$36 - 18 - 8 \sqrt{3} + 27 \sqrt{3}$

$\left(36 - 18\right) + \left(- 8 + 27\right) \sqrt{3}$

$18 + 19 \sqrt{3}$