Simplify 6(-7+6i)(-4+2i)

$6 (- 7 + 6 i) (- 4 + 2 i)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$(6 \cdot - 7 + 6 (6 i)) (- 4 + 2 i)$

Multiply.

Multiply $6$ by $- 7$ .

$(- 42 + 6 (6 i)) (- 4 + 2 i)$

Multiply $6$ by $6$ .

$(- 42 + 36 i) (- 4 + 2 i)$

Step 2

Expand $(- 42 + 36 i) (- 4 + 2 i)$ using the FOIL Method.

Apply the distributive property.

$- 42 (- 4 + 2 i) + 36 i (- 4 + 2 i)$

Apply the distributive property.

$- 42 \cdot - 4 - 42 (2 i) + 36 i (- 4 + 2 i)$

Apply the distributive property.

$- 42 \cdot - 4 - 42 (2 i) + 36 i \cdot - 4 + 36 i (2 i)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $- 42$ by $- 4$ .

$168 - 42 (2 i) + 36 i \cdot - 4 + 36 i (2 i)$

Multiply $2$ by $- 42$ .

$168 - 84 i + 36 i \cdot - 4 + 36 i (2 i)$

Multiply $- 4$ by $36$ .

$168 - 84 i - 144 i + 36 i (2 i)$

Multiply $36 i (2 i)$ .

Multiply $2$ by $36$ .

$168 - 84 i - 144 i + 72 i i$

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

$168 - 84 i - 144 i + 72 (i^{1} i)$

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

$168 - 84 i - 144 i + 72 (i^{1} i^{1})$

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

$168 - 84 i - 144 i + 72 i^{1 + 1}$

Add $1$ and $1$ .

$168 - 84 i - 144 i + 72 i^{2}$

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

$168 - 84 i - 144 i + 72 \cdot - 1$

Multiply $72$ by $- 1$ .

$168 - 84 i - 144 i - 72$

Subtract $72$ from $168$ .

$96 - 84 i - 144 i$

Subtract $144 i$ from $- 84 i$ .

$96 - 228 i$

Simplify 6(-7+6i)(-4+2i)

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