Algebra Examples

${(1 + i)}^{3}$

Step 1

Use the Binomial Theorem.

$1^{3} + 3 \cdot 1^{2} i + 3 \cdot 1 i^{2} + i^{3}$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

One to any power is one.

$1 + 3 \cdot 1^{2} i + 3 \cdot 1 i^{2} + i^{3}$

Step 2.1.2

One to any power is one.

$1 + 3 \cdot 1 i + 3 \cdot 1 i^{2} + i^{3}$

Step 2.1.3

Multiply $3$ by $1$ .

$1 + 3 i + 3 \cdot 1 i^{2} + i^{3}$

Step 2.1.4

Multiply $3$ by $1$ .

$1 + 3 i + 3 i^{2} + i^{3}$

Step 2.1.5

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

$1 + 3 i + 3 \cdot - 1 + i^{3}$

Step 2.1.6

Multiply $3$ by $- 1$ .

$1 + 3 i - 3 + i^{3}$

Step 2.1.7

Factor out $i^{2}$ .

$1 + 3 i - 3 + i^{2} \cdot i$

Step 2.1.8

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

$1 + 3 i - 3 - 1 \cdot i$

Step 2.1.9

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

$1 + 3 i - 3 - i$

$1 + 3 i - 3 - i$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $3$ from $1$ .

$- 2 + 3 i - i$

Step 2.2.2

Subtract $i$ from $3 i$ .

$- 2 + 2 i$

$- 2 + 2 i$

$- 2 + 2 i$

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