Precalculus Examples

$3 i^{7} (i - 5 i^{3})$

Step 1

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

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Step 1.1

Factor out $i^{4}$ .

$3 (i^{4} i^{3}) (i - 5 i^{3})$

Step 1.2

Factor out $i^{2}$ .

$3 (i^{4} (i^{2} \cdot i)) (i - 5 i^{3})$

$3 (i^{4} (i^{2} \cdot i)) (i - 5 i^{3})$

Step 2

Rewrite $i^{4}$ as $1$ .

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Step 2.1

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

$3 ({(i^{2})}^{2} (i^{2} \cdot i)) (i - 5 i^{3})$

Step 2.2

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

$3 ({(- 1)}^{2} (i^{2} \cdot i)) (i - 5 i^{3})$

Step 2.3

Raise $- 1$ to the power of $2$ .

$3 (1 (i^{2} \cdot i)) (i - 5 i^{3})$

$3 (1 (i^{2} \cdot i)) (i - 5 i^{3})$

Step 3

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

$3 (i^{2} \cdot i) (i - 5 i^{3})$

Step 4

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

$3 (- 1 \cdot i) (i - 5 i^{3})$

Step 5

Simplify the expression.

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Step 5.1

Rewrite $- 1 i$ as $- i$ .

$3 (- i) (i - 5 i^{3})$

Step 5.2

Multiply $- 1$ by $3$ .

$- 3 i (i - 5 i^{3})$

$- 3 i (i - 5 i^{3})$

Step 6

Simplify each term.

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Step 6.1

Factor out $i^{2}$ .

$- 3 i (i - 5 (i^{2} \cdot i))$

Step 6.2

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

$- 3 i (i - 5 (- 1 \cdot i))$

Step 6.3

Rewrite $- 1 i$ as $- i$ .

$- 3 i (i - 5 (- i))$

Step 6.4

Multiply $- 1$ by $- 5$ .

$- 3 i (i + 5 i)$

$- 3 i (i + 5 i)$

Step 7

Add $i$ and $5 i$ .

$- 3 i (6 i)$

Step 8

Multiply $- 3 i (6 i)$ .

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Step 8.1

Multiply $6$ by $- 3$ .

$- 18 i i$

Step 8.2

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

$- 18 (i^{1} i)$

Step 8.3

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

$- 18 (i^{1} i^{1})$

Step 8.4

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

$- 18 i^{1 + 1}$

Step 8.5

Add $1$ and $1$ .

$- 18 i^{2}$

$- 18 i^{2}$

Step 9

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

$- 18 \cdot - 1$

Step 10

Multiply $- 18$ by $- 1$ .

$18$

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