Calculus Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Factor $4$ out of $4 {(x + h)}^{2}$ .

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

Step 1.1.2

Factor $4$ out of $- 4 x^{2}$ .

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

Step 1.1.3

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

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

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 $a = x + h$ and $b = x$ .

$\frac{4 ((x + h + x) (x + h - x))}{h}$

Step 1.3

Simplify.

Tap for more steps...

Step 1.3.1

Add $x$ and $x$ .

$\frac{4 ((h + 2 x) (x + h - x))}{h}$

Step 1.3.2

Subtract $x$ from $x$ .

$\frac{4 ((h + 2 x) (h + 0))}{h}$

Step 1.3.3

Add $h$ and $0$ .

$\frac{4 ((h + 2 x) h)}{h}$

$\frac{4 (h + 2 x) h}{h}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Cancel the common factor of $h$ .

Tap for more steps...

Step 2.1.1

Cancel the common factor.

$\frac{4 (h + 2 x) h}{h}$

Step 2.1.2

Divide $4 (h + 2 x)$ by $1$ .

$4 (h + 2 x)$

Step 2.2

Apply the distributive property.

$4 h + 4 (2 x)$

Step 2.3

Multiply $2$ by $4$ .

$4 h + 8 x$