Simplify (-7-i)(-7+i)

$(- 7 - i) (- 7 + i)$

Step 1

Expand $(- 7 - i) (- 7 + i)$ using the FOIL Method.

Apply the distributive property.

$- 7 (- 7 + i) - i (- 7 + i)$

Apply the distributive property.

$- 7 \cdot - 7 - 7 i - i (- 7 + i)$

Apply the distributive property.

$- 7 \cdot - 7 - 7 i - i \cdot - 7 - i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 7$ by $- 7$ .

$49 - 7 i - i \cdot - 7 - i i$

Multiply $- 7$ by $- 1$ .

$49 - 7 i + 7 i - i i$

Multiply $- i i$ .

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

$49 - 7 i + 7 i - (i^{1} i)$

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

$49 - 7 i + 7 i - (i^{1} i^{1})$

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

$49 - 7 i + 7 i - i^{1 + 1}$

Add $1$ and $1$ .

$49 - 7 i + 7 i - i^{2}$

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

$49 - 7 i + 7 i - - 1$

Multiply $- 1$ by $- 1$ .

$49 - 7 i + 7 i + 1$

Add $49$ and $1$ .

$50 - 7 i + 7 i$

Add $- 7 i$ and $7 i$ .

$50 + 0$

Add $50$ and $0$ .

$50$