Finite Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{8}{x}$ .

$4 \frac{8^{2}}{x^{2}} - \frac{8}{x}$

Step 1.2

Raise $8$ to the power of $2$ .

$4 \frac{64}{x^{2}} - \frac{8}{x}$

Step 1.3

Multiply $4 \frac{64}{x^{2}}$ .

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Step 1.3.1

Combine $4$ and $\frac{64}{x^{2}}$ .

$\frac{4 \cdot 64}{x^{2}} - \frac{8}{x}$

Step 1.3.2

Multiply $4$ by $64$ .

$\frac{256}{x^{2}} - \frac{8}{x}$

Step 2

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

$\frac{256}{x^{2}} - \frac{8}{x} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{8}{x}$ by $\frac{x}{x}$ .

$\frac{256}{x^{2}} - \frac{8 x}{x \cdot x}$

Step 3.2

Raise $x$ to the power of $1$ .

$\frac{256}{x^{2}} - \frac{8 x}{x^{1} x}$

Step 3.3

Raise $x$ to the power of $1$ .

$\frac{256}{x^{2}} - \frac{8 x}{x^{1} x^{1}}$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{256}{x^{2}} - \frac{8 x}{x^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{256}{x^{2}} - \frac{8 x}{x^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{256 - 8 x}{x^{2}}$

Step 5

Factor $8$ out of $256 - 8 x$ .

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Step 5.1

Factor $8$ out of $256$ .

$\frac{8 (32) - 8 x}{x^{2}}$

Step 5.2

Factor $8$ out of $- 8 x$ .

$\frac{8 (32) + 8 (- x)}{x^{2}}$

Step 5.3

Factor $8$ out of $8 (32) + 8 (- x)$ .

$\frac{8 (32 - x)}{x^{2}}$