Simplify (i-2)^3-(i-2)

${(i - 2)}^{3} - (i - 2)$

Simplify each term.

Use the Binomial Theorem.

$i^{3} + 3 i^{2} \cdot - 2 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

Simplify each term.

Factor out $i^{2}$ .

$i^{2} \cdot i + 3 i^{2} \cdot - 2 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

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

$- 1 \cdot i + 3 i^{2} \cdot - 2 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

Rewrite $- 1 i$ as $- i$ .

$- i + 3 i^{2} \cdot - 2 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

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

$- i + 3 \cdot - 1 \cdot - 2 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

Multiply $3$ by $- 1$ .

$- i - 3 \cdot - 2 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

Multiply $- 3$ by $- 2$ .

$- i + 6 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

Raise $- 2$ to the power of $2$ .

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

Multiply $4$ by $3$ .

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

Raise $- 2$ to the power of $3$ .

$- i + 6 + 12 i - 8 - (i - 2)$

Add $- i$ and $12 i$ .

$6 + 11 i - 8 - (i - 2)$

Subtract $8$ from $6$ .

$- 2 + 11 i - (i - 2)$

Apply the distributive property.

$- 2 + 11 i - i - - 2$

Multiply $- 1$ by $- 2$ .

$- 2 + 11 i - i + 2$

Simplify by adding terms.

Add $- 2$ and $2$ .

$0 + 11 i - i$

Add $0$ and $11 i$ .

$11 i - i$

Subtract $i$ from $11 i$ .

$10 i$