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Question
Multiply: \[\left( - \frac{a}{7} + \frac{a^2}{9} \right)by\left( \frac{b}{2} - \frac{b^2}{3} \right)\].
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Solution
To multiply, we will use distributive law as follows:
\[\left( - \frac{a}{7} + \frac{a^2}{9} \right)\left( \frac{b}{2} - \frac{b^2}{3} \right)\]
\[ = \left( - \frac{a}{7} \right)\left( \frac{b}{2} - \frac{b^2}{3} \right) + \left( \frac{a^2}{9} \right)\left( \frac{b}{2} - \frac{b^2}{3} \right)\]
\[ = \left( - \frac{ab}{14} + \frac{a b^2}{21} \right) + \left( \frac{a^2 b}{18} - \frac{a^2 b^2}{27} \right)\]
\[ = - \frac{ab}{14} + \frac{a b^2}{21} + \frac{a^2 b}{18} - \frac{a^2 b^2}{27}\]
Thus, the answer is \[- \frac{ab}{14} + \frac{a b^2}{21} + \frac{a^2 b}{18} - \frac{a^2 b^2}{27}\].
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