Simplify (-6+i)(-6-i)

$(- 6 + i) (- 6 - i)$

Step 1

Expand $(- 6 + i) (- 6 - i)$ using the FOIL Method.

Apply the distributive property.

$- 6 (- 6 - i) + i (- 6 - i)$

Apply the distributive property.

$- 6 \cdot - 6 - 6 (- i) + i (- 6 - i)$

Apply the distributive property.

$- 6 \cdot - 6 - 6 (- i) + i \cdot - 6 + i (- i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 6$ by $- 6$ .

$36 - 6 (- i) + i \cdot - 6 + i (- i)$

Multiply $- 1$ by $- 6$ .

$36 + 6 i + i \cdot - 6 + i (- i)$

Move $- 6$ to the left of $i$ .

$36 + 6 i - 6 \cdot i + i (- i)$

Multiply $i (- i)$ .

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

$36 + 6 i - 6 i - (i^{1} i)$

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

$36 + 6 i - 6 i - (i^{1} i^{1})$

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

$36 + 6 i - 6 i - i^{1 + 1}$

Add $1$ and $1$ .

$36 + 6 i - 6 i - i^{2}$

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

$36 + 6 i - 6 i - - 1$

Multiply $- 1$ by $- 1$ .

$36 + 6 i - 6 i + 1$

Add $36$ and $1$ .

$37 + 6 i - 6 i$

Subtract $6 i$ from $6 i$ .

$37 + 0$

Add $37$ and $0$ .

$37$