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Question
Find the following product:
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Solution
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`.
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