Algebra Examples

$x i^{8} - y i^{6}$

Step 1

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$x {(i^{4})}^{2} - y i^{6}$

Step 2

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

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Step 2.1

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

$x {({(i^{2})}^{2})}^{2} - y i^{6}$

Step 2.2

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

$x {({(- 1)}^{2})}^{2} - y i^{6}$

Step 2.3

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

$x \cdot 1^{2} - y i^{6}$

$x \cdot 1^{2} - y i^{6}$

Step 3

One to any power is one.

$x \cdot 1 - y i^{6}$

Step 4

Multiply $x$ by $1$ .

$x - y i^{6}$

Step 5

Factor out $i^{4}$ .

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

Step 6

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

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Step 6.1

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

$x - y ({(i^{2})}^{2} i^{2})$

Step 6.2

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

$x - y ({(- 1)}^{2} i^{2})$

Step 6.3

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

$x - y (1 i^{2})$

$x - y (1 i^{2})$

Step 7

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

$x - y i^{2}$

Step 8

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

$x - y \cdot - 1$

Step 9

Multiply $- y \cdot - 1$ .

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Step 9.1

Multiply $- 1$ by $- 1$ .

$x + 1 y$

Step 9.2

Multiply $y$ by $1$ .

$x + y$

$x + y$

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