Finite Math Examples

$y = \frac{1}{4} \cdot {(x + 3)}^{3} - 5$

Step 1

Simplify each term.

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Step 1.1

Use the Binomial Theorem.

$y = \frac{1}{4} \cdot (x^{3} + 3 x^{2} \cdot 3 + 3 x \cdot 3^{2} + 3^{3}) - 5$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $3$ by $3$ .

$y = \frac{1}{4} \cdot (x^{3} + 9 x^{2} + 3 x \cdot 3^{2} + 3^{3}) - 5$

Step 1.2.2

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 1.2.2.1

Move $3^{2}$ .

$y = \frac{1}{4} \cdot (x^{3} + 9 x^{2} + 3^{2} \cdot 3 x + 3^{3}) - 5$

Step 1.2.2.2

Multiply $3^{2}$ by $3$ .

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Step 1.2.2.2.1

Raise $3$ to the power of $1$ .

$y = \frac{1}{4} \cdot (x^{3} + 9 x^{2} + 3^{2} \cdot 3^{1} x + 3^{3}) - 5$

Step 1.2.2.2.2

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

$y = \frac{1}{4} \cdot (x^{3} + 9 x^{2} + 3^{2 + 1} x + 3^{3}) - 5$

Step 1.2.2.3

Add $2$ and $1$ .

$y = \frac{1}{4} \cdot (x^{3} + 9 x^{2} + 3^{3} x + 3^{3}) - 5$

Step 1.2.3

Raise $3$ to the power of $3$ .

$y = \frac{1}{4} \cdot (x^{3} + 9 x^{2} + 27 x + 3^{3}) - 5$

Step 1.2.4

Raise $3$ to the power of $3$ .

$y = \frac{1}{4} \cdot (x^{3} + 9 x^{2} + 27 x + 27) - 5$

Step 1.3

Apply the distributive property.

$y = \frac{1}{4} x^{3} + \frac{1}{4} (9 x^{2}) + \frac{1}{4} (27 x) + \frac{1}{4} \cdot 27 - 5$

Step 1.4

Simplify.

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Step 1.4.1

Combine $\frac{1}{4}$ and $x^{3}$ .

$y = \frac{x^{3}}{4} + \frac{1}{4} (9 x^{2}) + \frac{1}{4} (27 x) + \frac{1}{4} \cdot 27 - 5$

Step 1.4.2

Multiply $\frac{1}{4} (9 x^{2})$ .

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Step 1.4.2.1

Combine $9$ and $\frac{1}{4}$ .

$y = \frac{x^{3}}{4} + \frac{9}{4} x^{2} + \frac{1}{4} (27 x) + \frac{1}{4} \cdot 27 - 5$

Step 1.4.2.2

Combine $\frac{9}{4}$ and $x^{2}$ .

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{1}{4} (27 x) + \frac{1}{4} \cdot 27 - 5$

Step 1.4.3

Multiply $\frac{1}{4} (27 x)$ .

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Step 1.4.3.1

Combine $27$ and $\frac{1}{4}$ .

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{27}{4} x + \frac{1}{4} \cdot 27 - 5$

Step 1.4.3.2

Combine $\frac{27}{4}$ and $x$ .

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{27 x}{4} + \frac{1}{4} \cdot 27 - 5$

Step 1.4.4

Combine $\frac{1}{4}$ and $27$ .

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{27 x}{4} + \frac{27}{4} - 5$

Step 2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{27 x}{4} + \frac{27}{4} - 5 \cdot \frac{4}{4}$

Step 3

Combine $- 5$ and $\frac{4}{4}$ .

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{27 x}{4} + \frac{27}{4} + \frac{- 5 \cdot 4}{4}$

Step 4

Combine the numerators over the common denominator.

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{27 x}{4} + \frac{27 - 5 \cdot 4}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 5$ by $4$ .

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{27 x}{4} + \frac{27 - 20}{4}$

Step 5.2

Subtract $20$ from $27$ .

$y = \frac{x^{3}}{4} + \frac{9 x^{2}}{4} + \frac{27 x}{4} + \frac{7}{4}$