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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 4$ by $- 4$ .

$16 - 4 (- i) + i \cdot - 4 + i (- i)$

Multiply $- 1$ by $- 4$ .

$16 + 4 i + i \cdot - 4 + i (- i)$

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

$16 + 4 i - 4 \cdot i + i (- i)$

Multiply $i (- i)$ .

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

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

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

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

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

$16 + 4 i - 4 i - i^{1 + 1}$

Add $1$ and $1$ .

$16 + 4 i - 4 i - i^{2}$

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

$16 + 4 i - 4 i - - 1$

Multiply $- 1$ by $- 1$ .

$16 + 4 i - 4 i + 1$

Add $16$ and $1$ .

$17 + 4 i - 4 i$

Subtract $4 i$ from $4 i$ .

$17 + 0$

Add $17$ and $0$ .

$17$