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.

$4 \cdot 4 + 4 i - i \cdot 4 - i i$

$4 \cdot 4 + 4 i - i \cdot 4 - i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

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

Multiply $4$ by $- 1$ .

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

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 $1$ .

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

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

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

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

Multiply $- 1$ by $- 1$ .

$16 + 4 i - 4 i + 1$

$16 + 4 i - 4 i + 1$

Add $16$ and $1$ .

$17 + 4 i - 4 i$

Subtract $4 i$ from $4 i$ .

$17 + 0$

Add $17$ and $0$ .

$17$

$17$

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