Simplify (2-i)(-3+6i)

$(2 - i) (- 3 + 6 i)$

Step 1

Expand $(2 - i) (- 3 + 6 i)$ using the FOIL Method.

Apply the distributive property.

$2 (- 3 + 6 i) - i (- 3 + 6 i)$

Apply the distributive property.

$2 \cdot - 3 + 2 (6 i) - i (- 3 + 6 i)$

Apply the distributive property.

$2 \cdot - 3 + 2 (6 i) - i \cdot - 3 - i (6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $- 3$ .

$- 6 + 2 (6 i) - i \cdot - 3 - i (6 i)$

Multiply $6$ by $2$ .

$- 6 + 12 i - i \cdot - 3 - i (6 i)$

Multiply $- 3$ by $- 1$ .

$- 6 + 12 i + 3 i - i (6 i)$

Multiply $- i (6 i)$ .

Multiply $6$ by $- 1$ .

$- 6 + 12 i + 3 i - 6 i i$

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

$- 6 + 12 i + 3 i - 6 (i^{1} i)$

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

$- 6 + 12 i + 3 i - 6 (i^{1} i^{1})$

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

$- 6 + 12 i + 3 i - 6 i^{1 + 1}$

Add $1$ and $1$ .

$- 6 + 12 i + 3 i - 6 i^{2}$

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

$- 6 + 12 i + 3 i - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$- 6 + 12 i + 3 i + 6$

Add $- 6$ and $6$ .

$0 + 12 i + 3 i$

Add $0$ and $12 i$ .

$12 i + 3 i$

Add $12 i$ and $3 i$ .

$15 i$