Pre-Algebra Examples

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

Step 1

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

$(x - \frac{1}{3}) (x - \frac{1}{3})$

Step 2

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

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Step 2.1

Apply the distributive property.

$x (x - \frac{1}{3}) - \frac{1}{3} (x - \frac{1}{3})$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Multiply $- \frac{1}{3} (- \frac{1}{3})$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.4.2

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

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

Step 3.1.4.3

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

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

Step 3.1.4.4

Multiply $3$ by $3$ .

$x^{2} - \frac{x}{3} - \frac{x}{3} + \frac{1}{9}$

Step 3.2

Subtract $\frac{x}{3}$ from $- \frac{x}{3}$ .

$x^{2} - 2 \frac{x}{3} + \frac{1}{9}$

Step 4

Simplify each term.

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Step 4.1

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

$x^{2} + \frac{- 2 x}{3} + \frac{1}{9}$

Step 4.2

Move the negative in front of the fraction.

$x^{2} - \frac{2 x}{3} + \frac{1}{9}$