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 $- 1$ by $4$ .

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

Move $4$ to the left of $i$ .

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

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 $1$ .

$17 - 4 i + 4 i$

Add $- 4 i$ and $4 i$ .

$17 + 0$

Add $17$ and $0$ .

$17$

$17$

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