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Question
Find the following product: \[\left( y^2 + \frac{5}{7} \right)\left( y^2 - \frac{14}{5} \right)\]
Solution
Here, we will use the identity \[\left( x + a \right)\left( x - b \right) = x^2 + \left( a - b \right)x - ab\].
\[\left( y^2 + \frac{5}{7} \right)\left( y^2 - \frac{14}{5} \right)\]
\[ = \left( y^2 \right)^2 + \left( \frac{5}{7} - \frac{14}{5} \right)\left( y^2 \right) - \frac{5}{7} \times \frac{14}{5}\]
\[ = y^4 - \frac{73}{35} y^2 - 2\]
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