Precalculus Examples

${(4 - i)}^{2}$

Step 1

Rewrite ${(4 - i)}^{2}$ as $(4 - i) (4 - i)$ .

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

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 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $4$ by $4$ .

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

Step 3.1.2

Multiply $- 1$ by $4$ .

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

Step 3.1.3

Multiply $4$ by $- 1$ .

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

Step 3.1.4

Multiply $- i (- i)$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.4.2

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

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

Step 3.1.4.3

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

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

Step 3.1.4.4

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

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

Step 3.1.4.5

Add $1$ and $1$ .

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

Step 3.1.4.6

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

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

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

Step 3.1.5

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

$16 - 4 i - 4 i - 1$

$16 - 4 i - 4 i - 1$

Step 3.2

Subtract $1$ from $16$ .

$15 - 4 i - 4 i$

Step 3.3

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

$15 - 8 i$

$15 - 8 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$