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 $4$ .

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

Multiply $4$ by $- 1$ .

$16 - 4 i - 4 i - i (- i)$

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

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

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

$16 - 4 i - 4 i + 1 (i^{1} i)$

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

$16 - 4 i - 4 i + 1 (i^{1} i^{1})$

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

$16 - 4 i - 4 i + 1 i^{1 + 1}$

Add $1$ and $1$ .

$16 - 4 i - 4 i + 1 i^{2}$

Multiply $i^{2}$ by $1$ .

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

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

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

$16 - 4 i - 4 i - 1$

$16 - 4 i - 4 i - 1$

Subtract $1$ from $16$ .

$15 - 4 i - 4 i$

Subtract $4 i$ from $- 4 i$ .

$15 - 8 i$

$15 - 8 i$

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