Simplify 2i(2i-i^3)

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

Step 1

Simplify each term.

Factor out $i^{2}$ .

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

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

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

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

$2 i (2 i - - i)$

Multiply $- 1$ by $- 1$ .

$2 i (2 i + 1 i)$

Multiply $i$ by $1$ .

$2 i (2 i + i)$

Step 2

Add $2 i$ and $i$ .

$2 i (3 i)$

Step 3

Multiply $2 i (3 i)$ .

Multiply $3$ by $2$ .

$6 i i$

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

$6 (i^{1} i)$

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

$6 (i^{1} i^{1})$

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

$6 i^{1 + 1}$

Add $1$ and $1$ .

$6 i^{2}$

Step 4

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

$6 \cdot - 1$

Step 5

Multiply $6$ by $- 1$ .

$- 6$