Answer
$z^2-\frac{7}{3}z+\frac{10}{9}$.
Work Step by Step
The given expression is
$=(z-\frac{5}{3})(z-\frac{2}{3})$
Use the FOIL method.
$=z(z)+z(-\frac{2}{3})-\frac{5}{3}(z)-\frac{5}{3}(-\frac{2}{3})$
Multiply.
$=z^2-\frac{2}{3}z-\frac{5}{3}z+\frac{10}{9}$
Combine like terms.
$=z^2-\frac{7}{3}z+\frac{10}{9}$
Hence, the product is $z^2-\frac{7}{3}z+\frac{10}{9}$.