Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Factor out $i^{2}$ .

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

Step 1.2

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

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

Step 1.3

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

$- i - i (2 - i)$

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $2$ by $- 1$ .

$- i - 2 i - i (- i)$

Step 1.6

Multiply $- i (- i)$ .

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$- i - 2 i + 1 i i$

Step 1.6.2

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

$- i - 2 i + 1 (i^{1} i)$

Step 1.6.3

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

$- i - 2 i + 1 (i^{1} i^{1})$

Step 1.6.4

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

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

Step 1.6.5

Add $1$ and $1$ .

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

Step 1.6.6

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

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

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

Step 1.7

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

$- i - 2 i - 1$

$- i - 2 i - 1$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 i$ from $- i$ .

$- 3 i - 1$

Step 2.2

Reorder $- 3 i$ and $- 1$ .

$- 1 - 3 i$

$- 1 - 3 i$

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