Basic Math Examples

$(p - \frac{1}{3}) (p + \frac{1}{3})$

Step 1

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

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Step 1.1

Apply the distributive property.

$p (p + \frac{1}{3}) - \frac{1}{3} (p + \frac{1}{3})$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$p \cdot p + p \frac{1}{3} - \frac{1}{3} p - \frac{1}{3} \cdot \frac{1}{3}$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $p \cdot p + p \frac{1}{3} - \frac{1}{3} p - \frac{1}{3} \cdot \frac{1}{3}$ .

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Step 2.1.1

Reorder the factors in the terms $p \frac{1}{3}$ and $- \frac{1}{3} p$ .

$p \cdot p + \frac{1}{3} p - \frac{1}{3} p - \frac{1}{3} \cdot \frac{1}{3}$

Step 2.1.2

Subtract $\frac{1}{3} p$ from $\frac{1}{3} p$ .

$p \cdot p + 0 - \frac{1}{3} \cdot \frac{1}{3}$

Step 2.1.3

Add $p \cdot p$ and $0$ .

$p \cdot p - \frac{1}{3} \cdot \frac{1}{3}$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $p$ by $p$ .

$p^{2} - \frac{1}{3} \cdot \frac{1}{3}$

Step 2.2.2

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

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Step 2.2.2.1

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

$p^{2} - \frac{1}{3 \cdot 3}$

Step 2.2.2.2

Multiply $3$ by $3$ .

$p^{2} - \frac{1}{9}$