# How do you simplify (8-6i)(-4-4i)?

Dec 3, 2016

$- 56 - 8 i$

#### Explanation:

$\left(\textcolor{red}{8} \textcolor{b l u e}{- 6 i}\right) \left(\textcolor{m a \ge n t a}{- 4} \textcolor{g r e e n}{- 4 i}\right)$

Multiply each term in the first expression by each term in the second expression (or FOIL).

$\left(\textcolor{red}{8} \cdot \textcolor{m a \ge n t a}{- 4}\right) + \left(\textcolor{red}{8} \cdot \textcolor{g r e e n}{- 4 i}\right) + \left(\textcolor{b l u e}{- 6 i} \cdot \textcolor{m a \ge n t a}{- 4}\right) + \left(\textcolor{b l u e}{- 6 i} \cdot \textcolor{g r e e n}{- 4 i}\right)$

$- 32 - 32 i + 24 i + 24 {i}^{2}$

Combine like terms

$- 32 - 8 i + 24 {i}^{2}$

Recall that ${i}^{2} = - 1$

$- 32 - 8 i + 24 \left(- 1\right)$

$- 32 - 8 i - 24$

Again, combine like terms

$- 56 - 8 i$