Basic Math Examples

$(\frac{1}{4} a + 7) (\frac{1}{4} a - 7)$

Step 1

Combine fractions.

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Step 1.1

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

$(\frac{a}{4} + 7) (\frac{1}{4} a - 7)$

Step 1.2

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

$(\frac{a}{4} + 7) (\frac{a}{4} - 7)$

Step 2

Expand $(\frac{a}{4} + 7) (\frac{a}{4} - 7)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\frac{a}{4} (\frac{a}{4} - 7) + 7 (\frac{a}{4} - 7)$

Step 2.2

Apply the distributive property.

$\frac{a}{4} \cdot \frac{a}{4} + \frac{a}{4} \cdot - 7 + 7 (\frac{a}{4} - 7)$

Step 2.3

Apply the distributive property.

$\frac{a}{4} \cdot \frac{a}{4} + \frac{a}{4} \cdot - 7 + 7 \frac{a}{4} + 7 \cdot - 7$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $\frac{a}{4} \cdot \frac{a}{4} + \frac{a}{4} \cdot - 7 + 7 \frac{a}{4} + 7 \cdot - 7$ .

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Step 3.1.1

Reorder the factors in the terms $\frac{a}{4} \cdot - 7$ and $7 \frac{a}{4}$ .

$\frac{a}{4} \cdot \frac{a}{4} - 7 \frac{a}{4} + 7 \frac{a}{4} + 7 \cdot - 7$

Step 3.1.2

Add $- 7 \frac{a}{4}$ and $7 \frac{a}{4}$ .

$\frac{a}{4} \cdot \frac{a}{4} + 0 + 7 \cdot - 7$

Step 3.1.3

Add $\frac{a}{4} \cdot \frac{a}{4}$ and $0$ .

$\frac{a}{4} \cdot \frac{a}{4} + 7 \cdot - 7$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $\frac{a}{4} \cdot \frac{a}{4}$ .

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Step 3.2.1.1

Multiply $\frac{a}{4}$ by $\frac{a}{4}$ .

$\frac{a \cdot a}{4 \cdot 4} + 7 \cdot - 7$

Step 3.2.1.2

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

$\frac{a^{1} a}{4 \cdot 4} + 7 \cdot - 7$

Step 3.2.1.3

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

$\frac{a^{1} a^{1}}{4 \cdot 4} + 7 \cdot - 7$

Step 3.2.1.4

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

$\frac{a^{1 + 1}}{4 \cdot 4} + 7 \cdot - 7$

Step 3.2.1.5

Add $1$ and $1$ .

$\frac{a^{2}}{4 \cdot 4} + 7 \cdot - 7$

Step 3.2.1.6

Multiply $4$ by $4$ .

$\frac{a^{2}}{16} + 7 \cdot - 7$

Step 3.2.2

Multiply $7$ by $- 7$ .

$\frac{a^{2}}{16} - 49$