Simplify -6i(8-6i)(-8-8i)

$- 6 i (8 - 6 i) (- 8 - 8 i)$

Step 1

Apply the distributive property.

$(- 6 i \cdot 8 - 6 i (- 6 i)) (- 8 - 8 i)$

Step 2

Multiply $8$ by $- 6$ .

$(- 48 i - 6 i (- 6 i)) (- 8 - 8 i)$

Step 3

Multiply $- 6 i (- 6 i)$ .

Multiply $- 6$ by $- 6$ .

$(- 48 i + 36 i i) (- 8 - 8 i)$

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

$(- 48 i + 36 (i^{1} i)) (- 8 - 8 i)$

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

$(- 48 i + 36 (i^{1} i^{1})) (- 8 - 8 i)$

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

$(- 48 i + 36 i^{1 + 1}) (- 8 - 8 i)$

Add $1$ and $1$ .

$(- 48 i + 36 i^{2}) (- 8 - 8 i)$

Step 4

Simplify each term.

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

$(- 48 i + 36 \cdot - 1) (- 8 - 8 i)$

Multiply $36$ by $- 1$ .

$(- 48 i - 36) (- 8 - 8 i)$

Step 5

Expand $(- 48 i - 36) (- 8 - 8 i)$ using the FOIL Method.

Apply the distributive property.

$- 48 i (- 8 - 8 i) - 36 (- 8 - 8 i)$

Apply the distributive property.

$- 48 i \cdot - 8 - 48 i (- 8 i) - 36 (- 8 - 8 i)$

Apply the distributive property.

$- 48 i \cdot - 8 - 48 i (- 8 i) - 36 \cdot - 8 - 36 (- 8 i)$

Step 6

Simplify and combine like terms.

Simplify each term.

Multiply $- 8$ by $- 48$ .

$384 i - 48 i (- 8 i) - 36 \cdot - 8 - 36 (- 8 i)$

Multiply $- 48 i (- 8 i)$ .

Multiply $- 8$ by $- 48$ .

$384 i + 384 i i - 36 \cdot - 8 - 36 (- 8 i)$

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

$384 i + 384 (i^{1} i) - 36 \cdot - 8 - 36 (- 8 i)$

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

$384 i + 384 (i^{1} i^{1}) - 36 \cdot - 8 - 36 (- 8 i)$

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

$384 i + 384 i^{1 + 1} - 36 \cdot - 8 - 36 (- 8 i)$

Add $1$ and $1$ .

$384 i + 384 i^{2} - 36 \cdot - 8 - 36 (- 8 i)$

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

$384 i + 384 \cdot - 1 - 36 \cdot - 8 - 36 (- 8 i)$

Multiply $384$ by $- 1$ .

$384 i - 384 - 36 \cdot - 8 - 36 (- 8 i)$

Multiply $- 36$ by $- 8$ .

$384 i - 384 + 288 - 36 (- 8 i)$

Multiply $- 8$ by $- 36$ .

$384 i - 384 + 288 + 288 i$

Add $384 i$ and $288 i$ .

$- 384 + 288 + 672 i$

Add $- 384$ and $288$ .

$- 96 + 672 i$

Simplify -6i(8-6i)(-8-8i)

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