Algebra Examples

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

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 $1$ .

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

Step 6

Apply the distributive property.

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

Step 7

Multiply $2$ by $- 2$ .

$2 x^{2} - 4$