Question

Subtract: 

\[x^2 y - \frac{4}{5}x y^2 + \frac{4}{3}xy \text { from } \frac{2}{3} x^2 y + \frac{3}{2}x y^2 - \frac{1}{3}xy\]

Answer 1

\[ \left( \frac{2}{3} x^2 y + \frac{3}{2}x y^2 - \frac{1}{3}xy \right) - \left( x^2 y - \frac{4}{5}x y^2 + \frac{4}{3}xy \right)\]

\[ = \frac{2}{3} x^2 y + \frac{3}{2}x y^2 - \frac{1}{3}xy - x^2 y + \frac{4}{5}x y^2 - \frac{4}{3}xy\]

\[ = \frac{2}{3} x^2 y - x^2 y + \frac{3}{2}x y^2 + \frac{4}{5}x y^2 - \frac{1}{3}xy - \frac{4}{3}xy (\text { Collecting like terms })\]

\[ = - \frac{1}{3} x^2 y + \frac{23}{10}x y^2 - \frac{5}{3}xy (\text { Combining like terms })\]