# How do you simplify (1-4i)(2+i)?

Apr 7, 2018

$5 - 7 i$

#### Explanation:

Keep in mind that ${i}^{2} = - 1$, and proceed, multiplying this with a method resembling FOIL:

$\left(1 - 4 i\right) \left(2 + i\right) = 1 + i - \left(4\right) \left(2\right) i - 4 {i}^{2}$

$1 + i - 8 i - 4 {i}^{2}$

Combine the like terms in the middle.
$1 - 7 i - 4 {i}^{2}$

$1 - 7 i - \left(4 \cdot - 1\right) = 5 - 7 i$

Apr 7, 2018

$6 - 7 i$

#### Explanation:

$\left(1 - 4 i\right) \left(2 + i\right) = 1 \times \left(2 + i\right) - 4 i \times \left(2 + i\right)$
$q \quad = 1 \times 2 + 1 \times i - 4 i \times 2 - 4 i \times i$
$q \quad = 2 + i - 8 i - 4 {i}^{2} = 2 - 7 i + 4 = 6 - 7 i$