Simplify (-5+i)(-5-i)

$(- 5 + i) (- 5 - i)$

Step 1

Expand $(- 5 + i) (- 5 - i)$ using the FOIL Method.

Apply the distributive property.

$- 5 (- 5 - i) + i (- 5 - i)$

Apply the distributive property.

$- 5 \cdot - 5 - 5 (- i) + i (- 5 - i)$

Apply the distributive property.

$- 5 \cdot - 5 - 5 (- i) + i \cdot - 5 + i (- i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 5$ by $- 5$ .

$25 - 5 (- i) + i \cdot - 5 + i (- i)$

Multiply $- 1$ by $- 5$ .

$25 + 5 i + i \cdot - 5 + i (- i)$

Move $- 5$ to the left of $i$ .

$25 + 5 i - 5 \cdot i + i (- i)$

Multiply $i (- i)$ .

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

$25 + 5 i - 5 i - (i^{1} i)$

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

$25 + 5 i - 5 i - (i^{1} i^{1})$

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

$25 + 5 i - 5 i - i^{1 + 1}$

Add $1$ and $1$ .

$25 + 5 i - 5 i - i^{2}$

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

$25 + 5 i - 5 i - - 1$

Multiply $- 1$ by $- 1$ .

$25 + 5 i - 5 i + 1$

Add $25$ and $1$ .

$26 + 5 i - 5 i$

Subtract $5 i$ from $5 i$ .

$26 + 0$

Add $26$ and $0$ .

$26$