Question 31: Calculate the value of the expression \(\begin{array}{l} C = \left( { – 2{x^2}{y^2} + 4xy – 6x{y^3}} \right) :\frac{2}{3}xy \end{array}\) at \(x=\frac{1}{2}\); y=4 is:

\(\begin{array}{l} C = \left( { – 2{x^2}{y^2} + 4xy – 6x{y^3}} \right):\frac{2}{3} xy\\ = – 2{x^2}{y^2}:\frac{2}{3}xy + 4xy:\frac{2}{3}xy – 6x{y^3}:\frac{2 }{3}xy\\ = – 3xy + 6 – 9{y^2} \end{array}\)

Replace \(x=\frac{1}{2}\), y=4 into C we get

\(C = – 3.\frac{1}{2}.4 + 6 – {9.4^2} = – 144\)