Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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 $v$ by $v$ .

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

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

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Step 2.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.4.2

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

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

Step 2.1.4.3

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

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

Step 2.1.4.4

Multiply $3$ by $3$ .

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

Step 2.2

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

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

Move the negative in front of the fraction.

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