Question

Multiply:
(3x²y − 5xy²) by  \[\left( \frac{1}{5} x^2 + \frac{1}{3} y^2 \right)\].

Answer 1

To multiply, we will use distributive law as follows:

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

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

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

Thus, the answer is \[\frac{3}{5} x^4 y - x^3 y^2 + x^2 y^3 - \frac{5}{3}x y^4\].