Simplify (8-i)(8+i)

$(8 - i) (8 + i)$

Step 1

Expand $(8 - i) (8 + i)$ using the FOIL Method.

Apply the distributive property.

$8 (8 + i) - i (8 + i)$

Apply the distributive property.

$8 \cdot 8 + 8 i - i (8 + i)$

Apply the distributive property.

$8 \cdot 8 + 8 i - i \cdot 8 - i i$

$8 \cdot 8 + 8 i - i \cdot 8 - i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $8$ .

$64 + 8 i - i \cdot 8 - i i$

Multiply $8$ by $- 1$ .

$64 + 8 i - 8 i - i i$

Multiply $- i i$ .

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

$64 + 8 i - 8 i - (i^{1} i)$

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

$64 + 8 i - 8 i - (i^{1} i^{1})$

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

$64 + 8 i - 8 i - i^{1 + 1}$

Add $1$ and $1$ .

$64 + 8 i - 8 i - i^{2}$

$64 + 8 i - 8 i - i^{2}$

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

$64 + 8 i - 8 i - - 1$

Multiply $- 1$ by $- 1$ .

$64 + 8 i - 8 i + 1$

$64 + 8 i - 8 i + 1$

Add $64$ and $1$ .

$65 + 8 i - 8 i$

Subtract $8 i$ from $8 i$ .

$65 + 0$

Add $65$ and $0$ .

$65$

$65$

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