Simplify (y+1/3)(y-1/3)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

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

Reorder the factors in the terms $y (- \frac{1}{3})$ and $\frac{1}{3} y$ .

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

Add $- \frac{1}{3} y$ and $\frac{1}{3} y$ .

$y \cdot y + 0 + \frac{1}{3} (- \frac{1}{3})$

Add $y \cdot y$ and $0$ .

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

Simplify each term.

Multiply $y$ by $y$ .

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

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

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

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

Multiply $3$ by $3$ .

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