Simplify (x+2/3)(x-1/3)

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

Step 1

Expand $(x + \frac{2}{3}) (x - \frac{1}{3})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

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

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

Multiply $\frac{2}{3} (- \frac{1}{3})$ .

Multiply $\frac{2}{3}$ by $\frac{1}{3}$ .

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

Multiply $3$ by $3$ .

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

Combine the numerators over the common denominator.

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

Step 3

Add $- x$ and $2 x$ .

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