# How do you simplify (-2-i)(4+i)?

Oct 2, 2016

$- 7 - 6 i$

#### Explanation:

$\left(- 2 - i\right) \left(4 + i\right)$

Distribute by multiplying each term in the first binomial by each term in the second binomial (i.e. FOIL).

$\left(- 2 \cdot 4\right) + \left(- 2 \cdot i\right) + \left(- i \cdot 4\right) + \left(- i \cdot i\right)$

$- 8 - 2 i - 4 i - {i}^{2} \textcolor{w h i t e}{a a a}$ Combine like terms

$- 8 - 6 i - {i}^{2} \textcolor{w h i t e}{a a a}$ Recall that ${i}^{2} = - 1$

$- 8 - 6 i - \left(- 1\right)$

$- 8 - 6 i + 1$

$- 7 - 6 i$