Algebra Examples

2 x^{- 3} (x^{5} - 2 x^{3})

$2 x^{- 3} (x^{5} - 2 x^{3})$

Step 1

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$2 \frac{1}{x^{3}} (x^{5} - 2 x^{3})$

Step 2

Combine

$2$ and

$\frac{1}{x^{3}}$ .

$\frac{2}{x^{3}} (x^{5} - 2 x^{3})$

Step 3

Multiply

$\frac{2}{x^{3}}$ by

$x^{5} - 2 x^{3}$ .

$\frac{2 (x^{5} - 2 x^{3})}{x^{3}}$

Step 4

Factor

$x^{3}$ out of

$x^{5} - 2 x^{3}$ .

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Step 4.1

Factor

$x^{3}$ out of

$x^{5}$ .

$\frac{2 (x^{3} x^{2} - 2 x^{3})}{x^{3}}$

Step 4.2

Factor

$x^{3}$ out of

$- 2 x^{3}$ .

$\frac{2 (x^{3} x^{2} + x^{3} \cdot - 2)}{x^{3}}$

Step 4.3

Factor

$x^{3}$ out of

$x^{3} x^{2} + x^{3} \cdot - 2$ .

$\frac{2 (x^{3} (x^{2} - 2))}{x^{3}}$

$\frac{2 x^{3} (x^{2} - 2)}{x^{3}}$

Step 5

Cancel the common factor of

$x^{3}$ .

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Step 5.1

Cancel the common factor.

$\frac{2 x^{3} (x^{2} - 2)}{x^{3}}$

Step 5.2

Divide

$2 (x^{2} - 2)$ by

$1$ .

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

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

Step 6

Apply the distributive property.

$2 x^{2} + 2 \cdot - 2$

Step 7

Multiply

$2$ by

$- 2$ .

$2 x^{2} - 4$

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