Algebra Examples

${(x + \frac{1}{x})}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $x$ .

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Step 2.1.1

Factor $x$ out of $3 x^{2}$ .

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

Apply the product rule to $\frac{1}{x}$ .

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

Step 2.3

Cancel the common factor of $x$ .

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Step 2.3.1

Factor $x$ out of $3 x$ .

$x^{3} + 3 x + x \cdot 3 \frac{1^{2}}{x^{2}} + {(\frac{1}{x})}^{3}$

Step 2.3.2

Factor $x$ out of $x^{2}$ .

$x^{3} + 3 x + x \cdot 3 \frac{1^{2}}{x \cdot x} + {(\frac{1}{x})}^{3}$

Step 2.3.3

Cancel the common factor.

$x^{3} + 3 x + x \cdot 3 \frac{1^{2}}{x \cdot x} + {(\frac{1}{x})}^{3}$

Step 2.3.4

Rewrite the expression.

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

Step 2.4

Combine $3$ and $\frac{1^{2}}{x}$ .

$x^{3} + 3 x + \frac{3 \cdot 1^{2}}{x} + {(\frac{1}{x})}^{3}$

Step 2.5

One to any power is one.

$x^{3} + 3 x + \frac{3 \cdot 1}{x} + {(\frac{1}{x})}^{3}$

Step 2.6

Multiply $3$ by $1$ .

$x^{3} + 3 x + \frac{3}{x} + {(\frac{1}{x})}^{3}$

Step 2.7

Apply the product rule to $\frac{1}{x}$ .

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

Step 2.8

One to any power is one.

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