Finite Math Examples

$- \frac{1}{12} \cdot ((x + 8) (x - 3))$

Step 1

Expand $(x + 8) (x - 3)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- \frac{1}{12} \cdot (x (x - 3) + 8 (x - 3))$

Step 1.2

Apply the distributive property.

$- \frac{1}{12} \cdot (x \cdot x + x \cdot - 3 + 8 (x - 3))$

Step 1.3

Apply the distributive property.

$- \frac{1}{12} \cdot (x \cdot x + x \cdot - 3 + 8 x + 8 \cdot - 3)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ .

$- \frac{1}{12} \cdot (x^{2} + x \cdot - 3 + 8 x + 8 \cdot - 3)$

Step 2.1.2

Move $- 3$ to the left of $x$ .

$- \frac{1}{12} \cdot (x^{2} - 3 \cdot x + 8 x + 8 \cdot - 3)$

Step 2.1.3

Multiply $8$ by $- 3$ .

$- \frac{1}{12} \cdot (x^{2} - 3 x + 8 x - 24)$

Step 2.2

Add $- 3 x$ and $8 x$ .

$- \frac{1}{12} \cdot (x^{2} + 5 x - 24)$

Step 3

Apply the distributive property.

$- \frac{1}{12} x^{2} - \frac{1}{12} (5 x) - \frac{1}{12} \cdot - 24$

Step 4

Simplify.

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Step 4.1

Combine $x^{2}$ and $\frac{1}{12}$ .

$- \frac{x^{2}}{12} - \frac{1}{12} (5 x) - \frac{1}{12} \cdot - 24$

Step 4.2

Multiply $- \frac{1}{12} (5 x)$ .

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Step 4.2.1

Multiply $5$ by $- 1$ .

$- \frac{x^{2}}{12} - 5 (\frac{1}{12}) x - \frac{1}{12} \cdot - 24$

Step 4.2.2

Combine $- 5$ and $\frac{1}{12}$ .

$- \frac{x^{2}}{12} + \frac{- 5}{12} x - \frac{1}{12} \cdot - 24$

Step 4.2.3

Combine $\frac{- 5}{12}$ and $x$ .

$- \frac{x^{2}}{12} + \frac{- 5 x}{12} - \frac{1}{12} \cdot - 24$

Step 4.3

Cancel the common factor of $12$ .

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Step 4.3.1

Move the leading negative in $- \frac{1}{12}$ into the numerator.

$- \frac{x^{2}}{12} + \frac{- 5 x}{12} + \frac{- 1}{12} \cdot - 24$

Step 4.3.2

Factor $12$ out of $- 24$ .

$- \frac{x^{2}}{12} + \frac{- 5 x}{12} + \frac{- 1}{12} \cdot (12 (- 2))$

Step 4.3.3

Cancel the common factor.

$- \frac{x^{2}}{12} + \frac{- 5 x}{12} + \frac{- 1}{12} \cdot (12 \cdot - 2)$

Step 4.3.4

Rewrite the expression.

$- \frac{x^{2}}{12} + \frac{- 5 x}{12} - 1 \cdot - 2$

Step 4.4

Multiply $- 1$ by $- 2$ .

$- \frac{x^{2}}{12} + \frac{- 5 x}{12} + 2$

Step 5

Move the negative in front of the fraction.

$- \frac{x^{2}}{12} - \frac{5 x}{12} + 2$