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Question
Find the following product: \[\left( x + \frac{1}{5} \right)(x + 5)\]
Solution
Here, we will use the identity \[\left( x + a \right)\left( x + b \right) = x^2 + \left( a + b \right)x + ab\].
\[\left( x + \frac{1}{5} \right)\left( x + 5 \right)\]
\[ = x^2 + \left( \frac{1}{5} + 5 \right)x + \frac{1}{5} \times 5\]
\[ = x^2 + \frac{26}{5}x + 1\]
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