Simplify (2+i)-(4-6i)(-3+3i)

$(2 + i) - (4 - 6 i) (- 3 + 3 i)$

Step 1

Simplify each term.

Apply the distributive property.

$2 + i + (- 1 \cdot 4 - (- 6 i)) (- 3 + 3 i)$

Multiply $- 1$ by $4$ .

$2 + i + (- 4 - (- 6 i)) (- 3 + 3 i)$

Multiply $- 6$ by $- 1$ .

$2 + i + (- 4 + 6 i) (- 3 + 3 i)$

Expand $(- 4 + 6 i) (- 3 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$2 + i - 4 (- 3 + 3 i) + 6 i (- 3 + 3 i)$

Apply the distributive property.

$2 + i - 4 \cdot - 3 - 4 (3 i) + 6 i (- 3 + 3 i)$

Apply the distributive property.

$2 + i - 4 \cdot - 3 - 4 (3 i) + 6 i \cdot - 3 + 6 i (3 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $- 4$ by $- 3$ .

$2 + i + 12 - 4 (3 i) + 6 i \cdot - 3 + 6 i (3 i)$

Multiply $3$ by $- 4$ .

$2 + i + 12 - 12 i + 6 i \cdot - 3 + 6 i (3 i)$

Multiply $- 3$ by $6$ .

$2 + i + 12 - 12 i - 18 i + 6 i (3 i)$

Multiply $6 i (3 i)$ .

Multiply $3$ by $6$ .

$2 + i + 12 - 12 i - 18 i + 18 i i$

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

$2 + i + 12 - 12 i - 18 i + 18 (i^{1} i)$

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

$2 + i + 12 - 12 i - 18 i + 18 (i^{1} i^{1})$

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

$2 + i + 12 - 12 i - 18 i + 18 i^{1 + 1}$

Add $1$ and $1$ .

$2 + i + 12 - 12 i - 18 i + 18 i^{2}$

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

$2 + i + 12 - 12 i - 18 i + 18 \cdot - 1$

Multiply $18$ by $- 1$ .

$2 + i + 12 - 12 i - 18 i - 18$

Subtract $18$ from $12$ .

$2 + i - 6 - 12 i - 18 i$

Subtract $18 i$ from $- 12 i$ .

$2 + i - 6 - 30 i$

Step 2

Simplify by adding terms.

Subtract $6$ from $2$ .

$- 4 + i - 30 i$

Subtract $30 i$ from $i$ .

$- 4 - 29 i$

Simplify (2+i)-(4-6i)(-3+3i)

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