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Question
Subtract:
\[x^2 y - \frac{4}{5}x y^2 + \frac{4}{3}xy \text { from } \frac{2}{3} x^2 y + \frac{3}{2}x y^2 - \frac{1}{3}xy\]
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Solution
\[ \left( \frac{2}{3} x^2 y + \frac{3}{2}x y^2 - \frac{1}{3}xy \right) - \left( x^2 y - \frac{4}{5}x y^2 + \frac{4}{3}xy \right)\]
\[ = \frac{2}{3} x^2 y + \frac{3}{2}x y^2 - \frac{1}{3}xy - x^2 y + \frac{4}{5}x y^2 - \frac{4}{3}xy\]
\[ = \frac{2}{3} x^2 y - x^2 y + \frac{3}{2}x y^2 + \frac{4}{5}x y^2 - \frac{1}{3}xy - \frac{4}{3}xy (\text { Collecting like terms })\]
\[ = - \frac{1}{3} x^2 y + \frac{23}{10}x y^2 - \frac{5}{3}xy (\text { Combining like terms })\]
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