Algebra Examples

$(\frac{1}{x} + 5) (3 x^{2} - 9)$

Step 1

Expand $(\frac{1}{x} + 5) (3 x^{2} - 9)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\frac{1}{x} (3 x^{2} - 9) + 5 (3 x^{2} - 9)$

Step 1.2

Apply the distributive property.

$\frac{1}{x} (3 x^{2}) + \frac{1}{x} \cdot - 9 + 5 (3 x^{2} - 9)$

Step 1.3

Apply the distributive property.

$\frac{1}{x} (3 x^{2}) + \frac{1}{x} \cdot - 9 + 5 (3 x^{2}) + 5 \cdot - 9$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$3 \frac{1}{x} x^{2} + \frac{1}{x} \cdot - 9 + 5 (3 x^{2}) + 5 \cdot - 9$

Step 2.1.2

Combine $3$ and $\frac{1}{x}$ .

$\frac{3}{x} x^{2} + \frac{1}{x} \cdot - 9 + 5 (3 x^{2}) + 5 \cdot - 9$

Step 2.1.3

Cancel the common factor of $x$ .

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Step 2.1.3.1

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

$\frac{3}{x} (x \cdot x) + \frac{1}{x} \cdot - 9 + 5 (3 x^{2}) + 5 \cdot - 9$

Step 2.1.3.2

Cancel the common factor.

$\frac{3}{x} (x \cdot x) + \frac{1}{x} \cdot - 9 + 5 (3 x^{2}) + 5 \cdot - 9$

Step 2.1.3.3

Rewrite the expression.

$3 x + \frac{1}{x} \cdot - 9 + 5 (3 x^{2}) + 5 \cdot - 9$

Step 2.1.4

Combine $\frac{1}{x}$ and $- 9$ .

$3 x + \frac{- 9}{x} + 5 (3 x^{2}) + 5 \cdot - 9$

Step 2.1.5

Move the negative in front of the fraction.

$3 x - \frac{9}{x} + 5 (3 x^{2}) + 5 \cdot - 9$

Step 2.1.6

Multiply $3$ by $5$ .

$3 x - \frac{9}{x} + 15 x^{2} + 5 \cdot - 9$

Step 2.1.7

Multiply $5$ by $- 9$ .

$3 x - \frac{9}{x} + 15 x^{2} - 45$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $- \frac{9}{x}$ .

$3 x + 15 x^{2} - \frac{9}{x} - 45$

Step 2.2.2

Reorder $3 x$ and $15 x^{2}$ .

$15 x^{2} + 3 x - \frac{9}{x} - 45$