Simplify (x-4i)^2

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

Step 1

Rewrite ${(x - 4 i)}^{2}$ as $(x - 4 i) (x - 4 i)$ .

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

Step 2

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 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

Multiply $- 4$ by $- 4$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $16$ by $- 1$ .

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

Move $i$ .

$x^{2} - 4 \cdot x i - 4 x i - 16$

Subtract $4 x i$ from $- 4 \cdot x i$ .

$x^{2} - 8 x i - 16$