Answer
$\Big(\dfrac{2}{5}y+\dfrac{1}{8}z\Big)\Big(\dfrac{3}{5}y+\dfrac{1}{2}z\Big)=\dfrac{6}{25}y^{2}+\dfrac{11}{40}yz+\dfrac{1}{16}z^{2}$
Work Step by Step
$\Big(\dfrac{2}{5}y+\dfrac{1}{8}z\Big)\Big(\dfrac{3}{5}y+\dfrac{1}{2}z\Big)$
Evaluate the binomial product using the FOIL method and simplify by combining like terms:
$\dfrac{2}{5}\cdot\dfrac{3}{5}y^{2}+\dfrac{2}{5}\cdot\dfrac{1}{2}yz+\dfrac{1}{8}\cdot\dfrac{3}{5}yz+\dfrac{1}{8}\cdot\dfrac{1}{2}z^{2}=...$
$...=\dfrac{6}{25}y^{2}+\dfrac{1}{5}yz+\dfrac{3}{40}yz+\dfrac{1}{16}z^{2}=...$
$...=\dfrac{6}{25}y^{2}+\dfrac{11}{40}yz+\dfrac{1}{16}z^{2}$
