Calculus Examples

$y (5) = {(5)}^{3} - 15 {(5)}^{2} + 75 (5) + 4$

Step 1

Simplify.

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Step 1.1

Raise $5$ to the power of $2$ .

$y (5) = 5^{3} - 15 \cdot 25 + 75 (5) + 4$

Step 1.2

Multiply $- 15$ by $25$ .

$y (5) = 5^{3} - 375 + 75 (5) + 4$

Step 1.3

Multiply $75$ by $5$ .

$y (5) = 5^{3} - 375 + 375 + 4$

Step 1.4

Add $- 375$ and $375$ .

$y (5) = 5^{3} + 0 + 4$

Step 1.5

Add $5^{3}$ and $0$ .

$y (5) = 5^{3} + 4$

Step 2

Divide each term in $y (5) = 5^{3} + 4$ by $5$ and simplify.

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Step 2.1

Divide each term in $y (5) = 5^{3} + 4$ by $5$ .

$\frac{y (5)}{5} = \frac{5^{3}}{5} + \frac{4}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{y \cdot 5}{5} = \frac{5^{3}}{5} + \frac{4}{5}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{5^{3}}{5} + \frac{4}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine the numerators over the common denominator.

$y = \frac{5^{3} + 4}{5}$

Step 2.3.2

Simplify the expression.

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Step 2.3.2.1

Raise $5$ to the power of $3$ .

$y = \frac{125 + 4}{5}$

Step 2.3.2.2

Add $125$ and $4$ .

$y = \frac{129}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{129}{5}$

Decimal Form:

$y = 25.8$

Mixed Number Form:

$y = 25 \frac{4}{5}$