Basic Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 1$ by $4$ .

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

Step 1.2

Use the Binomial Theorem.

$\frac{4 a^{3} - 4 (a^{3} + 3 a^{2} h + 3 a h^{2} + h^{3})}{h}$

Step 1.3

Apply the distributive property.

$\frac{4 a^{3} - 4 a^{3} - 4 (3 a^{2} h) - 4 (3 a h^{2}) - 4 h^{3}}{h}$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $3$ by $- 4$ .

$\frac{4 a^{3} - 4 a^{3} - 12 (a^{2} h) - 4 (3 a h^{2}) - 4 h^{3}}{h}$

Step 1.4.2

Multiply $3$ by $- 4$ .

$\frac{4 a^{3} - 4 a^{3} - 12 (a^{2} h) - 12 (a h^{2}) - 4 h^{3}}{h}$

Step 1.5

Remove parentheses.

$\frac{4 a^{3} - 4 a^{3} - 12 a^{2} h - 12 a h^{2} - 4 h^{3}}{h}$

Step 1.6

Subtract $4 a^{3}$ from $4 a^{3}$ .

$\frac{0 - 12 a^{2} h - 12 a h^{2} - 4 h^{3}}{h}$

Step 1.7

Subtract $12 a^{2} h$ from $0$ .

$\frac{- 12 a^{2} h - 12 a h^{2} - 4 h^{3}}{h}$

Step 1.8

Factor $4 h$ out of $- 12 a^{2} h - 12 a h^{2} - 4 h^{3}$ .

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Step 1.8.1

Factor $4 h$ out of $- 12 a^{2} h$ .

$\frac{4 h (- 3 a^{2}) - 12 a h^{2} - 4 h^{3}}{h}$

Step 1.8.2

Factor $4 h$ out of $- 12 a h^{2}$ .

$\frac{4 h (- 3 a^{2}) + 4 h (- 3 a h) - 4 h^{3}}{h}$

Step 1.8.3

Factor $4 h$ out of $- 4 h^{3}$ .

$\frac{4 h (- 3 a^{2}) + 4 h (- 3 a h) + 4 h (- h^{2})}{h}$

Step 1.8.4

Factor $4 h$ out of $4 h (- 3 a^{2}) + 4 h (- 3 a h)$ .

$\frac{4 h (- 3 a^{2} - 3 a h) + 4 h (- h^{2})}{h}$

Step 1.8.5

Factor $4 h$ out of $4 h (- 3 a^{2} - 3 a h) + 4 h (- h^{2})$ .

$\frac{4 h (- 3 a^{2} - 3 a h - h^{2})}{h}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $h$ .

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Step 2.1.1

Cancel the common factor.

$\frac{4 h (- 3 a^{2} - 3 a h - h^{2})}{h}$

Step 2.1.2

Divide $4 (- 3 a^{2} - 3 a h - h^{2})$ by $1$ .

$4 (- 3 a^{2} - 3 a h - h^{2})$

Step 2.2

Apply the distributive property.

$4 (- 3 a^{2}) + 4 (- 3 a h) + 4 (- h^{2})$

Step 3

Simplify.

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Step 3.1

Multiply $- 3$ by $4$ .

$- 12 a^{2} + 4 (- 3 a h) + 4 (- h^{2})$

Step 3.2

Multiply $- 3$ by $4$ .

$- 12 a^{2} - 12 (a h) + 4 (- h^{2})$

Step 3.3

Multiply $- 1$ by $4$ .

$- 12 a^{2} - 12 (a h) - 4 h^{2}$

$- 12 a^{2} - 12 a h - 4 h^{2}$