Algebra Examples

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

Step 1

Rewrite ${(\frac{x}{2} + 1)}^{2}$ as $(\frac{x}{2} + 1) (\frac{x}{2} + 1)$ .

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

Step 2

Expand $(\frac{x}{2} + 1) (\frac{x}{2} + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

$\frac{x}{2} \cdot \frac{x}{2} + \frac{x}{2} \cdot 1 + 1 \frac{x}{2} + 1 \cdot 1$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $\frac{x}{2} \cdot \frac{x}{2}$ .

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Step 3.1.1.1

Multiply $\frac{x}{2}$ by $\frac{x}{2}$ .

$\frac{x \cdot x}{2 \cdot 2} + \frac{x}{2} \cdot 1 + 1 \frac{x}{2} + 1 \cdot 1$

Step 3.1.1.2

Raise $x$ to the power of $1$ .

$\frac{x^{1} x}{2 \cdot 2} + \frac{x}{2} \cdot 1 + 1 \frac{x}{2} + 1 \cdot 1$

Step 3.1.1.3

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{1}}{2 \cdot 2} + \frac{x}{2} \cdot 1 + 1 \frac{x}{2} + 1 \cdot 1$

Step 3.1.1.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{1 + 1}}{2 \cdot 2} + \frac{x}{2} \cdot 1 + 1 \frac{x}{2} + 1 \cdot 1$

Step 3.1.1.5

Add $1$ and $1$ .

$\frac{x^{2}}{2 \cdot 2} + \frac{x}{2} \cdot 1 + 1 \frac{x}{2} + 1 \cdot 1$

Step 3.1.1.6

Multiply $2$ by $2$ .

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

Step 3.1.2

Multiply $\frac{x}{2}$ by $1$ .

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

Step 3.1.3

Multiply $\frac{x}{2}$ by $1$ .

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

Step 3.1.4

Multiply $1$ by $1$ .

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

Step 3.2

Add $\frac{x}{2}$ and $\frac{x}{2}$ .

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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