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Question
Multiply: \[\left( \frac{x}{7} + \frac{x^2}{2} \right)by\left( \frac{2}{5} + \frac{9x}{4} \right)\]
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Solution
To multiply the expressions, we will use the distributive law in the following way:
\[\left( \frac{x}{7} + \frac{x^2}{2} \right)\left( \frac{2}{5} + \frac{9x}{4} \right)\]
\[ = \frac{x}{7}\left( \frac{2}{5} + \frac{9x}{4} \right) + \frac{x^2}{2}\left( \frac{2}{5} + \frac{9x}{4} \right)\]
\[ = \frac{2x}{35} + \frac{9 x^2}{28} + \frac{x^2}{5} + \frac{9 x^3}{8}\]
\[ = \frac{2x}{35} + \left( \frac{45 + 28}{140} \right) x^2 + \frac{9 x^3}{8}\]
\[ = \frac{2x}{35} + \frac{73 x^2}{140} + \frac{9 x^2}{8}\]
Thus, the answer is \[\frac{2x}{35} + \frac{73 x^2}{140} + \frac{9 x^3}{8}\].
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