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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $x \cdot x + x (4 i) - 4 i x - 4 i (4 i)$ .

Reorder the factors in the terms $x (4 i)$ and $- 4 i x$ .

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

Subtract $4 i x$ from $4 i x$ .

$x \cdot x + 0 - 4 i (4 i)$

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $- 4 i (4 i)$ .

Multiply $4$ by $- 4$ .

$x^{2} - 16 i i$

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

$x^{2} - 16 (i^{1} i)$

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

$x^{2} - 16 (i^{1} i^{1})$

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

$x^{2} - 16 i^{1 + 1}$

Add $1$ and $1$ .

$x^{2} - 16 i^{2}$

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

$x^{2} - 16 \cdot - 1$

Multiply $- 16$ by $- 1$ .

$x^{2} + 16$