# How do you simplify (-2-3sqrt5)(5-sqrt5)?

Apr 1, 2018

$\implies 5 - 13 \sqrt{5}$

#### Explanation:

We are given:

$\left(\textcolor{b l u e}{- 2} \textcolor{red}{- 3 \sqrt{5}}\right) \left(\textcolor{\mathmr{and} a n \ge}{5} \textcolor{g r e e n}{- \sqrt{5}}\right)$

We need to multiply the two binomials. This means we multiply each term in one binomial by each term in the other.

$= \left(\textcolor{b l u e}{- 2}\right) \left(\textcolor{\mathmr{and} a n \ge}{5}\right) + \left(\textcolor{b l u e}{- 2}\right) \left(\textcolor{g r e e n}{- \sqrt{5}}\right) + \left(\textcolor{red}{- 3 \sqrt{5}}\right) \left(\textcolor{\mathmr{and} a n \ge}{5}\right) + \left(\textcolor{red}{- 3 \sqrt{5}}\right) \left(\textcolor{g r e e n}{- \sqrt{5}}\right)$

Now we simplify:

$= \left(- 10\right) + \left(2 \sqrt{5}\right) + \left(- 15 \sqrt{5}\right) + \left(3 \sqrt{5} \sqrt{5}\right)$

$= - 10 + 2 \sqrt{5} - 15 \sqrt{5} + 3 \left(5\right)$

$= - 10 + 2 \sqrt{5} - 15 \sqrt{5} + 15$

$= 5 - 13 \sqrt{5}$