Question

Find the following product:

\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]

Answer 1

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`.