Basic Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $a$ by $a$ .

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

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Step 3.1.4.1

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

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

Step 3.1.4.2

Multiply $2$ by $2$ .

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

Step 3.2

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

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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