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Question
Find the following product: \[\left( x + \frac{4}{3} \right)\left( x + \frac{3}{4} \right)\]
Solution
Here, we will use the identity \[\left( x + a \right)\left( x + b \right) = x^2 + \left( a + b \right)x + ab\].
\[\left( x + \frac{4}{3} \right)\left( x + \frac{3}{4} \right)\]
\[ = x^2 + \left( \frac{4}{3} + \frac{3}{4} \right)x + \frac{4}{3} \times \frac{3}{4}\]
\[ = x^2 + \frac{25}{12}x + 1\]
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