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Question
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
Solution
Given \[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
We shall use the identity `a^3 + b^3 = (a+b) (a^2 = ab + b^2)`,
we can rearrange the `(3 + 5/x)(9 - 15/x + 25/x^2)`as
`= (3+ 5/x) [(3)^2 - (3)(5/x)+ (5/x)^2]`
` = (3)^2 + (5/x)^3`
` = (3) xx (3) xx (3) + (5/x ) xx (5/x)xx (5/x)`
` = 27 + 125/x^3`
Hence the Product value of ` (3+ 5/x)(9- 15/x + 25/x^2)`is ` 27+ 125/x^3`.
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