Simplify i^3-i(2-i)

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

Simplify each term.

Factor out $i^{2}$ .

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

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

$- 1 \cdot i - i (2 - i)$

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

$- i - i (2 - i)$

Apply the distributive property.

$- i - i \cdot 2 - i (- i)$

Multiply $2$ by $- 1$ .

$- i - 2 i - i (- i)$

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

$- i - 2 i + 1 i i$

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

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

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

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

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

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

Add $1$ and $1$ .

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

Multiply $i^{2}$ by $1$ .

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

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

$- i - 2 i - 1$

Simplify by adding terms.

Subtract $2 i$ from $- i$ .

$- 3 i - 1$

Reorder $- 3 i$ and $- 1$ .

$- 1 - 3 i$