To multiply, we will use distributive law as follows: $\big(3\text{x}^2\text{y} − 5\text{xy}^2\big) \ \text{by} \ \big(\frac{1}{5}\text{x}^2 + \frac{1}{3}\text{y}^2\big)$ $=\frac{1}{5}\text{x}^2\big(3\text{x}^2\text{y}−5\text{xy}^2\big)+\frac{1}{3}\text{y}^2\big(3\text{x}^2\text{y}−5\text{xy}^2\big)$ $=\frac{3}{5}\text{x}^4\text{y}−\text{x}^3\text{y}^2+\text{x}^2\text{y}^3−\frac{5}{3}\text{xy}^4$ Thus, the answer is $=\frac{3}{5}\text{x}^4\text{y}−\text{x}^3\text{y}^2+\text{x}^2\text{y}^3−\frac{5}{3}\text{xy}^4.$
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