Basic Math Examples

$a^{3} - \frac{64}{a - 4}$

Step 1

To write $a^{3}$ as a fraction with a common denominator, multiply by $\frac{a - 4}{a - 4}$ .

$\frac{a^{3} (a - 4)}{a - 4} - \frac{64}{a - 4}$

Step 2

Combine the numerators over the common denominator.

$\frac{a^{3} (a - 4) - 64}{a - 4}$

Step 3

Rewrite $\frac{a^{3} (a - 4) - 64}{a - 4}$ in a factored form.

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Step 3.1

Apply the distributive property.

$\frac{a^{3} a + a^{3} \cdot - 4 - 64}{a - 4}$

Step 3.2

Multiply $a^{3}$ by $a$ by adding the exponents.

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Step 3.2.1

Multiply $a^{3}$ by $a$ .

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Step 3.2.1.1

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

$\frac{a^{3} a^{1} + a^{3} \cdot - 4 - 64}{a - 4}$

Step 3.2.1.2

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

$\frac{a^{3 + 1} + a^{3} \cdot - 4 - 64}{a - 4}$

Step 3.2.2

Add $3$ and $1$ .

$\frac{a^{4} + a^{3} \cdot - 4 - 64}{a - 4}$

Step 3.3

Move $- 4$ to the left of $a^{3}$ .

$\frac{a^{4} - 4 a^{3} - 64}{a - 4}$