Precalculus Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite ${(4 x + h)}^{2}$ as $(4 x + h) (4 x + h)$ .

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

Step 2.2

Expand $(4 x + h) (4 x + h)$ using the FOIL Method.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

Apply the distributive property.

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

Step 2.2.3

Apply the distributive property.

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

Step 2.3

Simplify and combine like terms.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.3.1.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.3.1.2.1

Move $x$ .

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

Step 2.3.1.2.2

Multiply $x$ by $x$ .

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

Step 2.3.1.3

Multiply $4$ by $4$ .

$\frac{16 x^{2} + 4 x h + h (4 x) + h \cdot h + 4 x + h - (4 x^{2} + 4 x)}{h}$

Step 2.3.1.4

Rewrite using the commutative property of multiplication.

$\frac{16 x^{2} + 4 x h + 4 h x + h \cdot h + 4 x + h - (4 x^{2} + 4 x)}{h}$

Step 2.3.1.5

Multiply $h$ by $h$ .

$\frac{16 x^{2} + 4 x h + 4 h x + h^{2} + 4 x + h - (4 x^{2} + 4 x)}{h}$

Step 2.3.2

Add $4 x h$ and $4 h x$ .

Tap for more steps...

Step 2.3.2.1

Move $x$ .

$\frac{16 x^{2} + 4 h x + 4 h x + h^{2} + 4 x + h - (4 x^{2} + 4 x)}{h}$

Step 2.3.2.2

Add $4 h x$ and $4 h x$ .

$\frac{16 x^{2} + 8 h x + h^{2} + 4 x + h - (4 x^{2} + 4 x)}{h}$

Step 2.4

Apply the distributive property.

$\frac{16 x^{2} + 8 h x + h^{2} + 4 x + h - (4 x^{2}) - (4 x)}{h}$

Step 2.5

Multiply $4$ by $- 1$ .

$\frac{16 x^{2} + 8 h x + h^{2} + 4 x + h - 4 x^{2} - (4 x)}{h}$

Step 2.6

Multiply $4$ by $- 1$ .

$\frac{16 x^{2} + 8 h x + h^{2} + 4 x + h - 4 x^{2} - 4 x}{h}$

Step 2.7

Subtract $4 x^{2}$ from $16 x^{2}$ .

$\frac{12 x^{2} + 8 h x + h^{2} + 4 x + h - 4 x}{h}$

Step 2.8

Subtract $4 x$ from $4 x$ .

$\frac{12 x^{2} + 8 h x + h^{2} + h + 0}{h}$

Step 2.9

Add $12 x^{2} + 8 h x + h^{2} + h$ and $0$ .

$\frac{12 x^{2} + 8 h x + h^{2} + h}{h}$