Algebra Examples

$2 i^{3} (5 - 12 i)$

Step 1

Factor out $i^{2}$ .

$2 (i^{2} \cdot i) (5 - 12 i)$

Step 2

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

$2 (- 1 \cdot i) (5 - 12 i)$

Step 3

Simplify the expression.

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Step 3.1

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

$2 (- i) (5 - 12 i)$

Step 3.2

Multiply $- 1$ by $2$ .

$- 2 i (5 - 12 i)$

$- 2 i (5 - 12 i)$

Step 4

Apply the distributive property.

$- 2 i \cdot 5 - 2 i (- 12 i)$

Step 5

Multiply $5$ by $- 2$ .

$- 10 i - 2 i (- 12 i)$

Step 6

Multiply $- 2 i (- 12 i)$ .

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Step 6.1

Multiply $- 12$ by $- 2$ .

$- 10 i + 24 i i$

Step 6.2

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

$- 10 i + 24 (i^{1} i)$

Step 6.3

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

$- 10 i + 24 (i^{1} i^{1})$

Step 6.4

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

$- 10 i + 24 i^{1 + 1}$

Step 6.5

Add $1$ and $1$ .

$- 10 i + 24 i^{2}$

$- 10 i + 24 i^{2}$

Step 7

Simplify each term.

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Step 7.1

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

$- 10 i + 24 \cdot - 1$

Step 7.2

Multiply $24$ by $- 1$ .

$- 10 i - 24$

$- 10 i - 24$

Step 8

Reorder $- 10 i$ and $- 24$ .

$- 24 - 10 i$

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