Question

This is expansion of Polynomial products and I just have to expand it but I dont know how to do it.

Answer 1

The expanded form of
`(x-(2)/(x) )  =  ((x+\sqrt2)(x-\sqrt2))/(x)`

Explanation:

Here, the given expression is
`(x-(2)/(x) )`

Expanding the given :

`(x-(2)/(x) ) = (x^2-2)/(x)`

Now, by ALGEBRAIC IDENTITY:

`(a+b)(a-b) =  a^2 - b^2\\\implies(x^2-2)  = (x-\sqrt2)(x+\sqrt2)`

So, the given expression becomes,

`(x^2 -2)/(x)  = ((x+\sqrt2)(x-\sqrt2))/(x)`

Hence, the expanded form of
`(x-(2)/(x) )  =  ((x+\sqrt2)(x-\sqrt2))/(x)`