Algebra Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $3 x^{2} \frac{1}{2}$ .

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

Move $3$ to the left of $x^{2}$ .

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

Step 2.3

Apply the product rule to $\frac{1}{2}$ .

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

Step 2.4

One to any power is one.

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

Step 2.5

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

$x^{3} + \frac{3 x^{2}}{2} + 3 x \frac{1}{4} + {(\frac{1}{2})}^{3}$

Step 2.6

Multiply $3 x \frac{1}{4}$ .

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Step 2.6.1

Combine $3$ and $\frac{1}{4}$ .

$x^{3} + \frac{3 x^{2}}{2} + x \frac{3}{4} + {(\frac{1}{2})}^{3}$

Step 2.6.2

Combine $x$ and $\frac{3}{4}$ .

$x^{3} + \frac{3 x^{2}}{2} + \frac{x \cdot 3}{4} + {(\frac{1}{2})}^{3}$

Step 2.7

Move $3$ to the left of $x$ .

$x^{3} + \frac{3 x^{2}}{2} + \frac{3 \cdot x}{4} + {(\frac{1}{2})}^{3}$

Step 2.8

Apply the product rule to $\frac{1}{2}$ .

$x^{3} + \frac{3 x^{2}}{2} + \frac{3 x}{4} + \frac{1^{3}}{2^{3}}$

Step 2.9

One to any power is one.

$x^{3} + \frac{3 x^{2}}{2} + \frac{3 x}{4} + \frac{1}{2^{3}}$

Step 2.10

Raise $2$ to the power of $3$ .

$x^{3} + \frac{3 x^{2}}{2} + \frac{3 x}{4} + \frac{1}{8}$