Pre-Algebra Examples

$3 x^{- 2} (3 x^{4} - 3 x^{2})$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 \frac{1}{x^{2}} (3 x^{4} - 3 x^{2})$

Step 2

Combine fractions.

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Step 2.1

Combine $3$ and $\frac{1}{x^{2}}$ .

$\frac{3}{x^{2}} (3 x^{4} - 3 x^{2})$

Step 2.2

Multiply $\frac{3}{x^{2}}$ by $3 x^{4} - 3 x^{2}$ .

$\frac{3 (3 x^{4} - 3 x^{2})}{x^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $3 x^{2}$ out of $3 x^{4} - 3 x^{2}$ .

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Step 3.1.1

Factor $3 x^{2}$ out of $3 x^{4}$ .

$\frac{3 (3 x^{2} (x^{2}) - 3 x^{2})}{x^{2}}$

Step 3.1.2

Factor $3 x^{2}$ out of $- 3 x^{2}$ .

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

Step 3.1.3

Factor $3 x^{2}$ out of $3 x^{2} (x^{2}) + 3 x^{2} (- 1)$ .

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

Step 3.2

Rewrite $1$ as $1^{2}$ .

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

Step 3.3

Factor.

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

Step 3.4

Multiply $3$ by $3$ .

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x^{2}$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Divide $(9 (x + 1)) (x - 1)$ by $1$ .

$(9 (x + 1)) (x - 1)$

Step 4.2

Apply the distributive property.

$(9 x + 9 \cdot 1) (x - 1)$

Step 4.3

Multiply $9$ by $1$ .

$(9 x + 9) (x - 1)$

Step 5

Expand $(9 x + 9) (x - 1)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$9 x (x - 1) + 9 (x - 1)$

Step 5.2

Apply the distributive property.

$9 x \cdot x + 9 x \cdot - 1 + 9 (x - 1)$

Step 5.3

Apply the distributive property.

$9 x \cdot x + 9 x \cdot - 1 + 9 x + 9 \cdot - 1$

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

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

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Step 6.1.1.1

Move $x$ .

$9 (x \cdot x) + 9 x \cdot - 1 + 9 x + 9 \cdot - 1$

Step 6.1.1.2

Multiply $x$ by $x$ .

$9 x^{2} + 9 x \cdot - 1 + 9 x + 9 \cdot - 1$

Step 6.1.2

Multiply $- 1$ by $9$ .

$9 x^{2} - 9 x + 9 x + 9 \cdot - 1$

Step 6.1.3

Multiply $9$ by $- 1$ .

$9 x^{2} - 9 x + 9 x - 9$

Step 6.2

Add $- 9 x$ and $9 x$ .

$9 x^{2} + 0 - 9$

Step 6.3

Add $9 x^{2}$ and $0$ .

$9 x^{2} - 9$