Answer
$\Big(\dfrac{3}{4}r-\dfrac{2}{3}s\Big)\Big(\dfrac{5}{4}r+\dfrac{1}{3}s\Big)=\dfrac{15}{16}r^{2}-\dfrac{7}{12}rs-\dfrac{2}{9}s^{2}$
Work Step by Step
$\Big(\dfrac{3}{4}r-\dfrac{2}{3}s\Big)\Big(\dfrac{5}{4}r+\dfrac{1}{3}s\Big)$
Evaluate the binomial product using the FOIL method and simplify by combining like terms:
$\dfrac{3}{4}\cdot\dfrac{5}{4}r^{2}+\dfrac{3}{4}\cdot\dfrac{1}{3}rs-\dfrac{2}{3}\cdot\dfrac{5}{4}rs-\dfrac{2}{3}\cdot\dfrac{1}{3}s^{2}=...$
$...=\dfrac{15}{16}r^{2}+\dfrac{1}{4}rs-\dfrac{5}{6}rs-\dfrac{2}{9}s^{2}=...$
$...=\dfrac{15}{16}r^{2}-\dfrac{7}{12}rs-\dfrac{2}{9}s^{2}$
