Basic Math Examples

$f ((8 x + 4) + h) - f (8 x + 4) \div h$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$f (8 x) + f \cdot 4 + f h - f (8 x + 4) \div h$

Step 1.2

Simplify.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$8 f x + f \cdot 4 + f h - f (8 x + 4) \div h$

Step 1.2.2

Move $4$ to the left of $f$ .

$8 f x + 4 \cdot f + f h - f (8 x + 4) \div h$

Step 1.3

Rewrite the division as a fraction.

$8 f x + 4 f + f h - \frac{f (8 x + 4)}{h}$

Step 1.4

Factor $4$ out of $8 x + 4$ .

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Step 1.4.1

Factor $4$ out of $8 x$ .

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

Step 1.4.2

Factor $4$ out of $4$ .

$8 f x + 4 f + f h - \frac{f (4 (2 x) + 4 (1))}{h}$

Step 1.4.3

Factor $4$ out of $4 (2 x) + 4 (1)$ .

$8 f x + 4 f + f h - \frac{f (4 (2 x + 1))}{h}$

$8 f x + 4 f + f h - \frac{f \cdot 4 (2 x + 1)}{h}$

Step 1.5

Move $4$ to the left of $f$ .

$8 f x + 4 f + f h - \frac{4 f (2 x + 1)}{h}$

Step 2

To write $8 f x$ as a fraction with a common denominator, multiply by $\frac{h}{h}$ .

$4 f + f h + \frac{8 f x h}{h} - \frac{4 f (2 x + 1)}{h}$

Step 3

Combine the numerators over the common denominator.

$4 f + f h + \frac{8 f x h - 4 f (2 x + 1)}{h}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $4 f$ out of $8 f x h - 4 f (2 x + 1)$ .

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Step 4.1.1

Factor $4 f$ out of $8 f x h$ .

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

Step 4.1.2

Factor $4 f$ out of $- 4 f (2 x + 1)$ .

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

Step 4.1.3

Factor $4 f$ out of $4 f (2 x h) + 4 f (- (2 x + 1))$ .

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

Step 4.2

Apply the distributive property.

$4 f + f h + \frac{4 f (2 x h - (2 x) - 1 \cdot 1)}{h}$

Step 4.3

Multiply $2$ by $- 1$ .

$4 f + f h + \frac{4 f (2 x h - 2 x - 1 \cdot 1)}{h}$

Step 4.4

Multiply $- 1$ by $1$ .

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

Step 5

To write $4 f$ as a fraction with a common denominator, multiply by $\frac{h}{h}$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Factor $4 f$ out of $4 f h + 4 f (2 x h - 2 x - 1)$ .

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Step 7.1.1

Factor $4 f$ out of $4 f h$ .

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

Step 7.1.2

Factor $4 f$ out of $4 f (h) + 4 f (2 x h - 2 x - 1)$ .

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

Step 7.2

Reorder terms.

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

Step 7.3

Factor out the greatest common factor from each group.

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Step 7.3.1

Group the first two terms and the last two terms.

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

Step 7.3.2

Factor out the greatest common factor (GCF) from each group.

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

Step 7.4

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

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

Step 8

To write $f h$ as a fraction with a common denominator, multiply by $\frac{h}{h}$ .

$\frac{f h \cdot h}{h} + \frac{4 f (2 x + 1) (h - 1)}{h}$

Step 9

Combine the numerators over the common denominator.

$\frac{f h \cdot h + 4 f (2 x + 1) (h - 1)}{h}$

Step 10

Simplify the numerator.

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Step 10.1

Factor $f$ out of $f h \cdot h + 4 f (2 x + 1) (h - 1)$ .

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Step 10.1.1

Factor $f$ out of $f h \cdot h$ .

$\frac{f (h \cdot h) + 4 f (2 x + 1) (h - 1)}{h}$

Step 10.1.2

Factor $f$ out of $4 f (2 x + 1) (h - 1)$ .

$\frac{f (h \cdot h) + f ((4 (2 x + 1)) (h - 1))}{h}$

Step 10.1.3

Factor $f$ out of $f (h \cdot h) + f ((4 (2 x + 1)) (h - 1))$ .

$\frac{f (h \cdot h + (4 (2 x + 1)) (h - 1))}{h}$

Step 10.2

Multiply $h$ by $h$ .

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

Step 10.3

Apply the distributive property.

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

Step 10.4

Multiply $2$ by $4$ .

$\frac{f (h^{2} + (8 x + 4 \cdot 1) (h - 1))}{h}$

Step 10.5

Multiply $4$ by $1$ .

$\frac{f (h^{2} + (8 x + 4) (h - 1))}{h}$

Step 10.6

Expand $(8 x + 4) (h - 1)$ using the FOIL Method.

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Step 10.6.1

Apply the distributive property.

$\frac{f (h^{2} + 8 x (h - 1) + 4 (h - 1))}{h}$

Step 10.6.2

Apply the distributive property.

$\frac{f (h^{2} + 8 x h + 8 x \cdot - 1 + 4 (h - 1))}{h}$

Step 10.6.3

Apply the distributive property.

$\frac{f (h^{2} + 8 x h + 8 x \cdot - 1 + 4 h + 4 \cdot - 1)}{h}$

Step 10.7

Simplify each term.

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Step 10.7.1

Multiply $- 1$ by $8$ .

$\frac{f (h^{2} + 8 x h - 8 x + 4 h + 4 \cdot - 1)}{h}$

Step 10.7.2

Multiply $4$ by $- 1$ .

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