Question

Multiply: \[\left( \frac{3}{5}x + \frac{1}{2}y \right) by \left( \frac{5}{6}x + 4y \right)\]

Answer 1

To multiply, we will use distributive law as follows:

\[\left( \frac{3}{5}x + \frac{1}{2}y \right)\left( \frac{5}{6}x + 4y \right)\]

\[ = \frac{3}{5}x\left( \frac{5}{6}x + 4y \right) + \frac{1}{2}y\left( \frac{5}{6}x + 4y \right)\]

\[ = \frac{1}{2} x^2 + \frac{12}{5}xy + \frac{5}{12}xy + 2 y^2 \]

\[ = \frac{1}{2} x^2 + \left( \frac{144 + 25}{60} \right)xy + 2 y^2 \]

\[ = \frac{1}{2} x^2 + \frac{169}{60}xy + 2 y^2\]

Thus, the answer is \[\frac{1}{2} x^2 + \frac{169}{60}xy + 2 y^2\].