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Question
Find the following product: \[\frac{7}{5} x^2 y\left( \frac{3}{5}x y^2 + \frac{2}{5}x \right)\]
Solution
To find the product, we will use distributive law as follows:
\[\frac{7}{5} x^2 y\left( \frac{3}{5}x y^2 + \frac{2}{5}x \right)\]
\[ = \frac{7}{5} x^2 y \times \frac{3}{5}x y^2 + \frac{7}{5} x^2 y \times \frac{2}{5}x\]
\[ = \frac{21}{25} x^{2 + 1} y^{1 + 2} + \frac{14}{25} x^{2 + 1} y\]
\[ = \frac{21}{25} x^3 y^3 + \frac{14}{25} x^3 y\]
Thus, the answer is \[\frac{21}{25} x^3 y^3 + \frac{14}{25} x^3 y\].
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