Simplify (8-3i)-(8-3i)(8+8i)

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

Step 1

Simplify each term.

Apply the distributive property.

$8 - 3 i + (- 1 \cdot 8 - (- 3 i)) (8 + 8 i)$

Multiply $- 1$ by $8$ .

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

Multiply $- 3$ by $- 1$ .

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

Expand $(- 8 + 3 i) (8 + 8 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$8 - 3 i - 8 \cdot 8 - 8 (8 i) + 3 i (8 + 8 i)$

Apply the distributive property.

$8 - 3 i - 8 \cdot 8 - 8 (8 i) + 3 i \cdot 8 + 3 i (8 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $- 8$ by $8$ .

$8 - 3 i - 64 - 8 (8 i) + 3 i \cdot 8 + 3 i (8 i)$

Multiply $8$ by $- 8$ .

$8 - 3 i - 64 - 64 i + 3 i \cdot 8 + 3 i (8 i)$

Multiply $8$ by $3$ .

$8 - 3 i - 64 - 64 i + 24 i + 3 i (8 i)$

Multiply $3 i (8 i)$ .

Multiply $8$ by $3$ .

$8 - 3 i - 64 - 64 i + 24 i + 24 i i$

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

$8 - 3 i - 64 - 64 i + 24 i + 24 (i^{1} i)$

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

$8 - 3 i - 64 - 64 i + 24 i + 24 (i^{1} i^{1})$

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

$8 - 3 i - 64 - 64 i + 24 i + 24 i^{1 + 1}$

Add $1$ and $1$ .

$8 - 3 i - 64 - 64 i + 24 i + 24 i^{2}$

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

$8 - 3 i - 64 - 64 i + 24 i + 24 \cdot - 1$

Multiply $24$ by $- 1$ .

$8 - 3 i - 64 - 64 i + 24 i - 24$

Subtract $24$ from $- 64$ .

$8 - 3 i - 88 - 64 i + 24 i$

Add $- 64 i$ and $24 i$ .

$8 - 3 i - 88 - 40 i$

Step 2

Simplify by adding terms.

Subtract $88$ from $8$ .

$- 80 - 3 i - 40 i$

Subtract $40 i$ from $- 3 i$ .

$- 80 - 43 i$

Simplify (8-3i)-(8-3i)(8+8i)

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