Question

Find the following product:

\[\left( \frac{2}{x} + 3x \right) \left( \frac{4}{x^2} + 9 x^2 - 6 \right)\]

Answer 1

Given  `(2/x + 3x) (4/x^2 + 9x^2 - 6)`

We shall use the identity, `a^3+ b^3 = (a+b) (a^2 + b^2 - ab)`

We can rearrange the `(2/x + 3x) (4/x^3 + 9x^2 - 6)`as

`= (2/x + 3x)[(2/x)^2 + (3x)^2 - (2/x) (3x)]`

` = (2/x^3) + (3x)^3`

`= (2/x) xx (2/x)  xx(2/x) + (3x) xx (3x) xx (3x)`

`= 8/x^3 + 27x^3`

Hence the Product value of  `(2/x + 3x) (4/x^2 + 9x^2 - 6)`is  `8/x^3 + 27x^3`.