Write in Standard Form 3i(2-i)(4+2i)

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

Apply the distributive property.

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

Multiply $2$ by $3$ .

$(6 i + 3 i (- i)) (4 + 2 i)$

Multiply $3 i (- i)$ .

Multiply $- 1$ by $3$ .

$(6 i - 3 i i) (4 + 2 i)$

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

$(6 i - 3 (i^{1} i)) (4 + 2 i)$

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

$(6 i - 3 (i^{1} i^{1})) (4 + 2 i)$

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

$(6 i - 3 i^{1 + 1}) (4 + 2 i)$

Add $1$ and $1$ .

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

Simplify each term.

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

$(6 i - 3 \cdot - 1) (4 + 2 i)$

Multiply $- 3$ by $- 1$ .

$(6 i + 3) (4 + 2 i)$

Expand $(6 i + 3) (4 + 2 i)$ using the FOIL Method.

Apply the distributive property.

$6 i (4 + 2 i) + 3 (4 + 2 i)$

Apply the distributive property.

$6 i \cdot 4 + 6 i (2 i) + 3 (4 + 2 i)$

Apply the distributive property.

$6 i \cdot 4 + 6 i (2 i) + 3 \cdot 4 + 3 (2 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $6$ .

$24 i + 6 i (2 i) + 3 \cdot 4 + 3 (2 i)$

Multiply $6 i (2 i)$ .

Multiply $2$ by $6$ .

$24 i + 12 i i + 3 \cdot 4 + 3 (2 i)$

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

$24 i + 12 (i^{1} i) + 3 \cdot 4 + 3 (2 i)$

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

$24 i + 12 (i^{1} i^{1}) + 3 \cdot 4 + 3 (2 i)$

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

$24 i + 12 i^{1 + 1} + 3 \cdot 4 + 3 (2 i)$

Add $1$ and $1$ .

$24 i + 12 i^{2} + 3 \cdot 4 + 3 (2 i)$

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

$24 i + 12 \cdot - 1 + 3 \cdot 4 + 3 (2 i)$

Multiply $12$ by $- 1$ .

$24 i - 12 + 3 \cdot 4 + 3 (2 i)$

Multiply $3$ by $4$ .

$24 i - 12 + 12 + 3 (2 i)$

Multiply $2$ by $3$ .

$24 i - 12 + 12 + 6 i$

Add $24 i$ and $6 i$ .

$- 12 + 12 + 30 i$

Add $- 12$ and $12$ .

$0 + 30 i$

Add $0$ and $30 i$ .

$30 i$

Write in Standard Form 3i(2-i)(4+2i)

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