Simplify (x-3)(x-4i)(x+4i)

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

Expand $(x - 3) (x - 4 i)$ using the FOIL Method.

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

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Multiply $x$ by $x$ .

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

Move $- 4$ to the left of $x$ .

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

Multiply $- 4$ by $- 3$ .

$(x^{2} - 4 x i - 3 x + 12 i) (x + 4 i)$

Expand $(x^{2} - 4 x i - 3 x + 12 i) (x + 4 i)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

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Simplify each term.

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Multiply $x^{2}$ by $x$ by adding the exponents.

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Multiply $x^{2}$ by $x$ .

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

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

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

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

Add $2$ and $1$ .

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

Move $4$ to the left of $x^{2}$ .

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

Multiply $x$ by $x$ by adding the exponents.

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Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 4 x i (4 i)$ .

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Multiply $4$ by $- 4$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i - 16 x i i - 3 x \cdot x - 3 x (4 i) + 12 i x + 12 i (4 i)$

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

$x^{3} + 4 x^{2} i - 4 x^{2} i - 16 x (i^{1} i) - 3 x \cdot x - 3 x (4 i) + 12 i x + 12 i (4 i)$

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

$x^{3} + 4 x^{2} i - 4 x^{2} i - 16 x (i^{1} i^{1}) - 3 x \cdot x - 3 x (4 i) + 12 i x + 12 i (4 i)$

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

$x^{3} + 4 x^{2} i - 4 x^{2} i - 16 x i^{1 + 1} - 3 x \cdot x - 3 x (4 i) + 12 i x + 12 i (4 i)$

Add $1$ and $1$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i - 16 x i^{2} - 3 x \cdot x - 3 x (4 i) + 12 i x + 12 i (4 i)$

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

$x^{3} + 4 x^{2} i - 4 x^{2} i - 16 x \cdot - 1 - 3 x \cdot x - 3 x (4 i) + 12 i x + 12 i (4 i)$

Multiply $- 1$ by $- 16$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x \cdot x - 3 x (4 i) + 12 i x + 12 i (4 i)$

Multiply $x$ by $x$ by adding the exponents.

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Move $x$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 (x \cdot x) - 3 x (4 i) + 12 i x + 12 i (4 i)$

Multiply $x$ by $x$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 3 x (4 i) + 12 i x + 12 i (4 i)$

Multiply $4$ by $- 3$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x + 12 i (4 i)$

Multiply $12 i (4 i)$ .

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Multiply $4$ by $12$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x + 48 i i$

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

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x + 48 (i^{1} i)$

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

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x + 48 (i^{1} i^{1})$

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

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x + 48 i^{1 + 1}$

Add $1$ and $1$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x + 48 i^{2}$

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

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x + 48 \cdot - 1$

Multiply $48$ by $- 1$ .

$x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x - 48$

Simplify by adding terms.

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Combine the opposite terms in $x^{3} + 4 x^{2} i - 4 x^{2} i + 16 x - 3 x^{2} - 12 x i + 12 i x - 48$ .

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Subtract $4 x^{2} i$ from $4 x^{2} i$ .

$x^{3} + 0 + 16 x - 3 x^{2} - 12 x i + 12 i x - 48$

Add $x^{3}$ and $0$ .

$x^{3} + 16 x - 3 x^{2} - 12 x i + 12 i x - 48$

Reorder the factors in the terms $- 12 x i$ and $12 i x$ .

$x^{3} + 16 x - 3 x^{2} - 12 i x + 12 i x - 48$

Add $- 12 i x$ and $12 i x$ .

$x^{3} + 16 x - 3 x^{2} + 0 - 48$

Add $x^{3} + 16 x - 3 x^{2}$ and $0$ .

$x^{3} + 16 x - 3 x^{2} - 48$

Move $16 x$ .

$x^{3} - 3 x^{2} + 16 x - 48$

Simplify (x-3)(x-4i)(x+4i)

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