Finite Math Examples

$5 {(\sqrt[3]{x^{2} - 9})}^{3} + 9$

Step 1

Simplify each term.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$5 {\sqrt[3]{x^{2} - 3^{2}}}^{3} + 9$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$5 {\sqrt[3]{(x + 3) (x - 3)}}^{3} + 9$

Step 1.3

Rewrite ${\sqrt[3]{(x + 3) (x - 3)}}^{3}$ as $(x + 3) (x - 3)$ .

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Step 1.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{(x + 3) (x - 3)}$ as ${((x + 3) (x - 3))}^{\frac{1}{3}}$ .

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

Step 1.3.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.3.3

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

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

Step 1.3.4

Cancel the common factor of $3$ .

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Step 1.3.4.1

Cancel the common factor.

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

Step 1.3.4.2

Rewrite the expression.

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

Step 1.3.5

Simplify.

$5 ((x + 3) (x - 3)) + 9$

Step 1.4

Expand $(x + 3) (x - 3)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$5 (x (x - 3) + 3 (x - 3)) + 9$

Step 1.4.2

Apply the distributive property.

$5 (x \cdot x + x \cdot - 3 + 3 (x - 3)) + 9$

Step 1.4.3

Apply the distributive property.

$5 (x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3) + 9$

Step 1.5

Combine the opposite terms in $x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$ .

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Step 1.5.1

Reorder the factors in the terms $x \cdot - 3$ and $3 x$ .

$5 (x \cdot x - 3 x + 3 x + 3 \cdot - 3) + 9$

Step 1.5.2

Add $- 3 x$ and $3 x$ .

$5 (x \cdot x + 0 + 3 \cdot - 3) + 9$

Step 1.5.3

Add $x \cdot x$ and $0$ .

$5 (x \cdot x + 3 \cdot - 3) + 9$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $x$ by $x$ .

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

Step 1.6.2

Multiply $3$ by $- 3$ .

$5 (x^{2} - 9) + 9$

Step 1.7

Apply the distributive property.

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

Step 1.8

Multiply $5$ by $- 9$ .

$5 x^{2} - 45 + 9$

Step 2

Add $- 45$ and $9$ .

$5 x^{2} - 36$