# How do you simplify (4-sqrt3)(12+5sqrt3)?

Feb 7, 2016

$33 + 8 \sqrt{3}$

#### Explanation:

Begin by expanding the brackets. By doing this we get:

$4 \cdot 12 + 4 \cdot 5 \sqrt{3} - \sqrt{3} \cdot 12 - \sqrt{3} \cdot 5 \sqrt{3}$

Now if we do the multiplications we get:

$48 + 20 \sqrt{3} - 12 \sqrt{3} - 15$

We can now simplify by gathering the like terms:

$33 + 8 \sqrt{3}$

Feb 7, 2016

Multiply everything with everything.

#### Explanation:

$\left(4 - \sqrt{3}\right) \left(12 + 5 \sqrt{3}\right)$

= $48 - 12 \sqrt{3} + 20 \sqrt{3} - 5 \sqrt{9}$

= $48 - 15 + 8 \sqrt{3}$

= $33 + 8 \sqrt{3}$

Practice exercises:

1. Simplify the following expressions.

a) $\left(3 - 2 \sqrt{5}\right) \left(4 + \sqrt{10}\right)$

b) $\left(4 \sqrt{6} + 5 \sqrt{11}\right) \left(3 \sqrt{7} - 9\right)$

c) $\left(2 + \sqrt{13}\right) \left(2 - \sqrt{13}\right)$

d) ${\left(\sqrt{2} - \sqrt{15}\right)}^{2}$