Algebra Examples

$(- 4 + i) (- 4 - i)$

Step 1

Expand $(- 4 + i) (- 4 - i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 4 (- 4 - i) + i (- 4 - i)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 4$ by $- 4$ .

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

Step 2.1.2

Multiply $- 1$ by $- 4$ .

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

Step 2.1.3

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

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

Step 2.1.4

Multiply $i (- i)$ .

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Step 2.1.4.1

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

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

Step 2.1.4.2

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

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

Step 2.1.4.3

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

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

Step 2.1.4.4

Add $1$ and $1$ .

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

Step 2.1.5

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

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

Step 2.1.6

Multiply $- 1$ by $- 1$ .

$16 + 4 i - 4 i + 1$

Step 2.2

Add $16$ and $1$ .

$17 + 4 i - 4 i$

Step 2.3

Subtract $4 i$ from $4 i$ .

$17 + 0$

Step 2.4

Add $17$ and $0$ .

$17$