Simplify 3i(2-i)^2

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

Step 1

Rewrite ${(2 - i)}^{2}$ as $(2 - i) (2 - i)$ .

$3 i ((2 - i) (2 - i))$

Step 2

Expand $(2 - i) (2 - i)$ using the FOIL Method.

Apply the distributive property.

$3 i (2 (2 - i) - i (2 - i))$

Apply the distributive property.

$3 i (2 \cdot 2 + 2 (- i) - i (2 - i))$

Apply the distributive property.

$3 i (2 \cdot 2 + 2 (- i) - i \cdot 2 - i (- i))$

$3 i (2 \cdot 2 + 2 (- i) - i \cdot 2 - i (- i))$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$3 i (4 + 2 (- i) - i \cdot 2 - i (- i))$

Multiply $- 1$ by $2$ .

$3 i (4 - 2 i - i \cdot 2 - i (- i))$

Multiply $2$ by $- 1$ .

$3 i (4 - 2 i - 2 i - i (- i))$

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

$3 i (4 - 2 i - 2 i + 1 i i)$

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

$3 i (4 - 2 i - 2 i + 1 (i^{1} i))$

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

$3 i (4 - 2 i - 2 i + 1 (i^{1} i^{1}))$

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

$3 i (4 - 2 i - 2 i + 1 i^{1 + 1})$

Add $1$ and $1$ .

$3 i (4 - 2 i - 2 i + 1 i^{2})$

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

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

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

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

$3 i (4 - 2 i - 2 i - 1)$

$3 i (4 - 2 i - 2 i - 1)$

Subtract $1$ from $4$ .

$3 i (3 - 2 i - 2 i)$

Subtract $2 i$ from $- 2 i$ .

$3 i (3 - 4 i)$

$3 i (3 - 4 i)$

Step 4

Apply the distributive property.

$3 i \cdot 3 + 3 i (- 4 i)$

Step 5

Multiply $3$ by $3$ .

$9 i + 3 i (- 4 i)$

Step 6

Multiply $3 i (- 4 i)$ .

Multiply $- 4$ by $3$ .

$9 i - 12 i i$

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

$9 i - 12 (i^{1} i)$

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

$9 i - 12 (i^{1} i^{1})$

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

$9 i - 12 i^{1 + 1}$

Add $1$ and $1$ .

$9 i - 12 i^{2}$

$9 i - 12 i^{2}$

Step 7

Simplify each term.

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

$9 i - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$9 i + 12$

$9 i + 12$

Step 8

Reorder $9 i$ and $12$ .

$12 + 9 i$

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