# How do you simplify (-5-i)(-2+2i)?

Jun 19, 2018

$12 - 8 i$

#### Explanation:

Like we would do with real numbers, we can multiply this out with FOIL (Firsts, Outsides, Insides, Lasts). This is the order we multiply in. We get

• First terms: $- 5 \cdot - 2 = 10$
• Outside terms: $- 5 \cdot 2 i = - 10 i$
• Inside terms: $- i \cdot - 2 = 2 i$
• Last terms: $- i \cdot 2 i = - 2 {i}^{2}$

This leaves us with

$- 2 {i}^{2} - 10 i + 2 i + 10$

Which can be simplified further as

$- 2 {i}^{2} - 8 i + 10$

Note that ${i}^{2} = - 1$, so we can plug in this value. We now have

$- 2 \left(- 1\right) - 8 i + 10$

Which finally simplifies to

$12 - 8 i$

Hope this helps!