Calculus Examples

$(x + 8) (\frac{24}{x} + 12)$

Step 1

Expand $(x + 8) (\frac{24}{x} + 12)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x (\frac{24}{x} + 12) + 8 (\frac{24}{x} + 12)$

Step 1.2

Apply the distributive property.

$x \frac{24}{x} + x \cdot 12 + 8 (\frac{24}{x} + 12)$

Step 1.3

Apply the distributive property.

$x \frac{24}{x} + x \cdot 12 + 8 \frac{24}{x} + 8 \cdot 12$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $x$ .

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Step 2.1.1.1

Cancel the common factor.

$x \frac{24}{x} + x \cdot 12 + 8 \frac{24}{x} + 8 \cdot 12$

Step 2.1.1.2

Rewrite the expression.

$24 + x \cdot 12 + 8 \frac{24}{x} + 8 \cdot 12$

Step 2.1.2

Move $12$ to the left of $x$ .

$24 + 12 \cdot x + 8 \frac{24}{x} + 8 \cdot 12$

Step 2.1.3

Multiply $8 \frac{24}{x}$ .

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Step 2.1.3.1

Combine $8$ and $\frac{24}{x}$ .

$24 + 12 x + \frac{8 \cdot 24}{x} + 8 \cdot 12$

Step 2.1.3.2

Multiply $8$ by $24$ .

$24 + 12 x + \frac{192}{x} + 8 \cdot 12$

Step 2.1.4

Multiply $8$ by $12$ .

$24 + 12 x + \frac{192}{x} + 96$

Step 2.2

Add $24$ and $96$ .

$12 x + \frac{192}{x} + 120$