Finite Math Examples

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

Step 1

Remove parentheses.

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

Step 2

Remove parentheses.

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

Step 3

Remove parentheses.

$y = \frac{1}{3} \cdot 2^{3} - 2^{2} + 2 + 2$

Step 4

Remove parentheses.

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

Step 5

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

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Step 5.1

Simplify each term.

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Step 5.1.1

Raise $2$ to the power of $3$ .

$y = \frac{1}{3} \cdot 8 - {(2)}^{2} + 2 + 2$

Step 5.1.2

Combine $\frac{1}{3}$ and $8$ .

$y = \frac{8}{3} - {(2)}^{2} + 2 + 2$

Step 5.1.3

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

$y = \frac{8}{3} - 1 \cdot 4 + 2 + 2$

Step 5.1.4

Multiply $- 1$ by $4$ .

$y = \frac{8}{3} - 4 + 2 + 2$

Step 5.2

Find the common denominator.

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Step 5.2.1

Write $- 4$ as a fraction with denominator $1$ .

$y = \frac{8}{3} + \frac{- 4}{1} + 2 + 2$

Step 5.2.2

Multiply $\frac{- 4}{1}$ by $\frac{3}{3}$ .

$y = \frac{8}{3} + \frac{- 4}{1} \cdot \frac{3}{3} + 2 + 2$

Step 5.2.3

Multiply $\frac{- 4}{1}$ by $\frac{3}{3}$ .

$y = \frac{8}{3} + \frac{- 4 \cdot 3}{3} + 2 + 2$

Step 5.2.4

Write $2$ as a fraction with denominator $1$ .

$y = \frac{8}{3} + \frac{- 4 \cdot 3}{3} + \frac{2}{1} + 2$

Step 5.2.5

Multiply $\frac{2}{1}$ by $\frac{3}{3}$ .

$y = \frac{8}{3} + \frac{- 4 \cdot 3}{3} + \frac{2}{1} \cdot \frac{3}{3} + 2$

Step 5.2.6

Multiply $\frac{2}{1}$ by $\frac{3}{3}$ .

$y = \frac{8}{3} + \frac{- 4 \cdot 3}{3} + \frac{2 \cdot 3}{3} + 2$

Step 5.2.7

Write $2$ as a fraction with denominator $1$ .

$y = \frac{8}{3} + \frac{- 4 \cdot 3}{3} + \frac{2 \cdot 3}{3} + \frac{2}{1}$

Step 5.2.8

Multiply $\frac{2}{1}$ by $\frac{3}{3}$ .

$y = \frac{8}{3} + \frac{- 4 \cdot 3}{3} + \frac{2 \cdot 3}{3} + \frac{2}{1} \cdot \frac{3}{3}$

Step 5.2.9

Multiply $\frac{2}{1}$ by $\frac{3}{3}$ .

$y = \frac{8}{3} + \frac{- 4 \cdot 3}{3} + \frac{2 \cdot 3}{3} + \frac{2 \cdot 3}{3}$

Step 5.3

Combine the numerators over the common denominator.

$y = \frac{8 - 4 \cdot 3 + 2 \cdot 3 + 2 \cdot 3}{3}$

Step 5.4

Simplify each term.

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Step 5.4.1

Multiply $- 4$ by $3$ .

$y = \frac{8 - 12 + 2 \cdot 3 + 2 \cdot 3}{3}$

Step 5.4.2

Multiply $2$ by $3$ .

$y = \frac{8 - 12 + 6 + 2 \cdot 3}{3}$

Step 5.4.3

Multiply $2$ by $3$ .

$y = \frac{8 - 12 + 6 + 6}{3}$

Step 5.5

Simplify by adding and subtracting.

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Step 5.5.1

Subtract $12$ from $8$ .

$y = \frac{- 4 + 6 + 6}{3}$

Step 5.5.2

Add $- 4$ and $6$ .

$y = \frac{2 + 6}{3}$

Step 5.5.3

Add $2$ and $6$ .

$y = \frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{8}{3}$

Decimal Form:

$y = 2.\overline{6}$

Mixed Number Form:

$y = 2 \frac{2}{3}$