# How do you simplify (-3-i)(2-2i)?

Oct 20, 2016

$- 8 + 4 i$

#### Explanation:

Multiply the brackets out as for normal algebra but replace ${i}^{2}$with $- 1$

$\left(- 3 - i\right) \left(2 - 2 i\right)$

multiplying out, and building up the expansion.

$\left(\textcolor{red}{- 3} - i\right) \left(\textcolor{red}{2} - 2 i\right)$

=$\textcolor{red}{- 6}$

$\left(\textcolor{red}{- 3} - i\right) \left(2 - \textcolor{red}{2 i}\right)$

=$- 6 - \left(\textcolor{red}{- 6 i}\right)$

$\left(- 3 - \textcolor{red}{i}\right) \left(\textcolor{red}{2} - 2 i\right)$

=$- 6 - \left(- 6 i\right) - \textcolor{red}{2 i}$

$\left(- 3 - \textcolor{red}{i}\right) \left(2 - \textcolor{red}{2 i}\right)$

=$- 6 - \left(- 6 i\right) - 2 i + \textcolor{red}{2 {i}^{2}}$

$= - 6 + 6 i - 2 i + 2 \times \left(- 1\right)$

$= - 6 + 6 i - 2 i - 2$

collecting like terms, putting the real part first , we have:

$- 8 + 4 i$