Precalculus Examples

$- 6 {(x + \frac{1}{3})}^{2} - \frac{20}{3}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x + \frac{1}{3})}^{2}$ as $(x + \frac{1}{3}) (x + \frac{1}{3})$ .

$- 6 ((x + \frac{1}{3}) (x + \frac{1}{3})) - \frac{20}{3}$

Step 1.2

Expand $(x + \frac{1}{3}) (x + \frac{1}{3})$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$- 6 (x (x + \frac{1}{3}) + \frac{1}{3} (x + \frac{1}{3})) - \frac{20}{3}$

Step 1.2.2

Apply the distributive property.

$- 6 (x \cdot x + x \frac{1}{3} + \frac{1}{3} (x + \frac{1}{3})) - \frac{20}{3}$

Step 1.2.3

Apply the distributive property.

$- 6 (x \cdot x + x \frac{1}{3} + \frac{1}{3} x + \frac{1}{3} \cdot \frac{1}{3}) - \frac{20}{3}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$- 6 (x^{2} + x \frac{1}{3} + \frac{1}{3} x + \frac{1}{3} \cdot \frac{1}{3}) - \frac{20}{3}$

Step 1.3.1.2

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

$- 6 (x^{2} + \frac{x}{3} + \frac{1}{3} x + \frac{1}{3} \cdot \frac{1}{3}) - \frac{20}{3}$

Step 1.3.1.3

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

$- 6 (x^{2} + \frac{x}{3} + \frac{x}{3} + \frac{1}{3} \cdot \frac{1}{3}) - \frac{20}{3}$

Step 1.3.1.4

Multiply $\frac{1}{3} \cdot \frac{1}{3}$ .

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Step 1.3.1.4.1

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

$- 6 (x^{2} + \frac{x}{3} + \frac{x}{3} + \frac{1}{3 \cdot 3}) - \frac{20}{3}$

Step 1.3.1.4.2

Multiply $3$ by $3$ .

$- 6 (x^{2} + \frac{x}{3} + \frac{x}{3} + \frac{1}{9}) - \frac{20}{3}$

Step 1.3.2

Add $\frac{x}{3}$ and $\frac{x}{3}$ .

$- 6 (x^{2} + 2 \frac{x}{3} + \frac{1}{9}) - \frac{20}{3}$

Step 1.4

Combine $2$ and $\frac{x}{3}$ .

$- 6 (x^{2} + \frac{2 x}{3} + \frac{1}{9}) - \frac{20}{3}$

Step 1.5

Apply the distributive property.

$- 6 x^{2} - 6 \frac{2 x}{3} - 6 (\frac{1}{9}) - \frac{20}{3}$

Step 1.6

Simplify.

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Step 1.6.1

Cancel the common factor of $3$ .

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Step 1.6.1.1

Factor $3$ out of $- 6$ .

$- 6 x^{2} + 3 (- 2) \frac{2 x}{3} - 6 (\frac{1}{9}) - \frac{20}{3}$

Step 1.6.1.2

Cancel the common factor.

$- 6 x^{2} + 3 \cdot - 2 \frac{2 x}{3} - 6 (\frac{1}{9}) - \frac{20}{3}$

Step 1.6.1.3

Rewrite the expression.

$- 6 x^{2} - 2 (2 x) - 6 (\frac{1}{9}) - \frac{20}{3}$

Step 1.6.2

Multiply $2$ by $- 2$ .

$- 6 x^{2} - 4 x - 6 (\frac{1}{9}) - \frac{20}{3}$

Step 1.6.3

Cancel the common factor of $3$ .

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Step 1.6.3.1

Factor $3$ out of $- 6$ .

$- 6 x^{2} - 4 x + 3 (- 2) \frac{1}{9} - \frac{20}{3}$

Step 1.6.3.2

Factor $3$ out of $9$ .

$- 6 x^{2} - 4 x + 3 \cdot - 2 \frac{1}{3 \cdot 3} - \frac{20}{3}$

Step 1.6.3.3

Cancel the common factor.

$- 6 x^{2} - 4 x + 3 \cdot - 2 \frac{1}{3 \cdot 3} - \frac{20}{3}$

Step 1.6.3.4

Rewrite the expression.

$- 6 x^{2} - 4 x - 2 (\frac{1}{3}) - \frac{20}{3}$

Step 1.6.4

Combine $- 2$ and $\frac{1}{3}$ .

$- 6 x^{2} - 4 x + \frac{- 2}{3} - \frac{20}{3}$

Step 1.7

Move the negative in front of the fraction.

$- 6 x^{2} - 4 x - \frac{2}{3} - \frac{20}{3}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$- 6 x^{2} - 4 x + \frac{- 2 - 20}{3}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $20$ from $- 2$ .

$- 6 x^{2} - 4 x + \frac{- 22}{3}$

Step 2.2.2

Move the negative in front of the fraction.

$- 6 x^{2} - 4 x - \frac{22}{3}$