Pre-Algebra Examples

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

Step 1

Rewrite the function as an equation.

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

Step 2

Simplify $3 {(x + \frac{1}{3})}^{2} - 4$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

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

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Step 2.1.2.1

Apply the distributive property.

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

Step 2.1.2.2

Apply the distributive property.

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

Step 2.1.2.3

Apply the distributive property.

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

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

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

Step 2.1.3.1.2

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

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

Step 2.1.3.1.3

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

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

Step 2.1.3.1.4

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

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Step 2.1.3.1.4.1

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

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

Step 2.1.3.1.4.2

Multiply $3$ by $3$ .

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

Step 2.1.3.2

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

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

Step 2.1.4

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

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

Step 2.1.5

Apply the distributive property.

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

Step 2.1.6

Simplify.

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Step 2.1.6.1

Cancel the common factor of $3$ .

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Step 2.1.6.1.1

Cancel the common factor.

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

Step 2.1.6.1.2

Rewrite the expression.

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

Step 2.1.6.2

Cancel the common factor of $3$ .

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Step 2.1.6.2.1

Factor $3$ out of $9$ .

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

Step 2.1.6.2.2

Cancel the common factor.

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

Step 2.1.6.2.3

Rewrite the expression.

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

Step 2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.3

Combine $- 4$ and $\frac{3}{3}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 4$ by $3$ .

$y = 3 x^{2} + 2 x + \frac{1 - 12}{3}$

Step 2.5.2

Subtract $12$ from $1$ .

$y = 3 x^{2} + 2 x + \frac{- 11}{3}$

Step 2.6

Move the negative in front of the fraction.

$y = 3 x^{2} + 2 x - \frac{11}{3}$