Answer
$x^2+\dfrac{1}{3}x-\dfrac{2}{9}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, then,
\begin{array}{l}
\left( x-\dfrac{1}{3} \right)\left( x+\dfrac{2}{3} \right)
\\\\=
x^2+\dfrac{2}{3}x-\dfrac{1}{3}x-\dfrac{2}{9}
\\\\=
x^2+\dfrac{1}{3}x-\dfrac{2}{9}
.\end{array}
