Evaluate 2(2+4i)(-3+i)

$2 (2 + 4 i) (- 3 + i)$

Simplify by multiplying through.

Apply the distributive property.

$(2 \cdot 2 + 2 (4 i)) (- 3 + i)$

Multiply.

Multiply $2$ by $2$ .

$(4 + 2 (4 i)) (- 3 + i)$

Multiply $4$ by $2$ .

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

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.

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

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 $- 1$ .

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

Subtract $8$ from $- 12$ .

$- 20 + 4 i - 24 i$

Subtract $24 i$ from $4 i$ .

$- 20 - 20 i$