Basic Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a + h$ and $b = a$ .

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

Step 1.3

Simplify.

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Step 1.3.1

Add $a$ and $a$ .

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

Step 1.3.2

Subtract $a$ from $a$ .

$\frac{3 ((2 a + h) (h + 0))}{h}$

Step 1.3.3

Add $h$ and $0$ .

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

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

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.

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

Step 2.1.2

Divide $3 (2 a + h)$ by $1$ .

$3 (2 a + h)$

Step 2.2

Apply the distributive property.

$3 (2 a) + 3 h$

Step 2.3

Multiply $2$ by $3$ .

$6 a + 3 h$