Simplify (-4-8i)(3+i)

$(- 4 - 8 i) (3 + i)$

Step 1

Expand $(- 4 - 8 i) (3 + i)$ using the FOIL Method.

Apply the distributive property.

$- 4 (3 + i) - 8 i (3 + i)$

Apply the distributive property.

$- 4 \cdot 3 - 4 i - 8 i (3 + i)$

Apply the distributive property.

$- 4 \cdot 3 - 4 i - 8 i \cdot 3 - 8 i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 4$ by $3$ .

$- 12 - 4 i - 8 i \cdot 3 - 8 i i$

Multiply $3$ by $- 8$ .

$- 12 - 4 i - 24 i - 8 i i$

Multiply $- 8 i i$ .

Raise $i$ to the power of $1$ .

$- 12 - 4 i - 24 i - 8 (i^{1} i)$

Raise $i$ to the power of $1$ .

$- 12 - 4 i - 24 i - 8 (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 12 - 4 i - 24 i - 8 i^{1 + 1}$

Add $1$ and $1$ .

$- 12 - 4 i - 24 i - 8 i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$- 12 - 4 i - 24 i - 8 \cdot - 1$

Multiply $- 8$ by $- 1$ .

$- 12 - 4 i - 24 i + 8$

Add $- 12$ and $8$ .

$- 4 - 4 i - 24 i$

Subtract $24 i$ from $- 4 i$ .

$- 4 - 28 i$