Calculus Examples

$\frac{(2 {(1 + h)}^{2} + 4) - (2 {(1)}^{2} + 4)}{h}$

Step 1

Simplify the numerator.

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Step 1.1

Let $u = 1$ . Substitute $u$ for all occurrences of $1$ .

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Step 1.1.1

Subtract $2 u^{2}$ from $2 u^{2}$ .

$\frac{4 h u + 2 h^{2} + 4 + 0 - 4}{h}$

Step 1.1.2

Add $4 h u + 2 h^{2} + 4$ and $0$ .

$\frac{4 h u + 2 h^{2} + 4 - 4}{h}$

Step 1.1.3

Subtract $4$ from $4$ .

$\frac{4 h u + 2 h^{2} + 0}{h}$

Step 1.1.4

Add $4 h u + 2 h^{2}$ and $0$ .

$\frac{4 h u + 2 h^{2}}{h}$

Step 1.2

Factor $2 h$ out of $4 h u + 2 h^{2}$ .

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Step 1.2.1

Factor $2 h$ out of $4 h u$ .

$\frac{2 h (2 u) + 2 h^{2}}{h}$

Step 1.2.2

Factor $2 h$ out of $2 h^{2}$ .

$\frac{2 h (2 u) + 2 h (h)}{h}$

Step 1.2.3

Factor $2 h$ out of $2 h (2 u) + 2 h (h)$ .

$\frac{2 h (2 u + h)}{h}$

Step 1.3

Replace all occurrences of $u$ with $1$ .

$\frac{2 h (2 \cdot 1 + h)}{h}$

Step 1.4

Multiply $2$ by $1$ .

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

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.

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

Step 2.1.2

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

$2 (2 + h)$

Step 2.2

Apply the distributive property.

$2 \cdot 2 + 2 h$

Step 2.3

Multiply $2$ by $2$ .

$4 + 2 h$