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Question
Multiply: \[\left( \frac{3}{5}x + \frac{1}{2}y \right) by \left( \frac{5}{6}x + 4y \right)\]
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Solution
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 \[\frac{1}{2} x^2 + \frac{169}{60}xy + 2 y^2\].
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