Answer
$x^{2}+\frac{1}{3}x-\frac{2}{9}$
Work Step by Step
Using the FOIL method, $(x-\frac{1}{3})(x+\frac{2}{3})=(x)(x)+(x)(\frac{2}{3})+(-\frac{1}{3})(x)+(-\frac{1}{3})(\frac{2}{3})=x^{2}+\frac{2}{3}x+(-\frac{1}{3}x)+(-\frac{2}{9})=x^{2}+\frac{2}{3}x-\frac{1}{3}x-\frac{2}{9}=x^{2}+(\frac{2}{3}-\frac{1}{3})x-\frac{2}{9}=x^{2}+\frac{1}{3}x-\frac{2}{9}$.
