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

Question

asked Dec 28, 2020 195k views

1 Answer

Naomy · Answer 1 · 2021-01-03T03:35:26+0000

Answer:

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
$(x-(2)/(x) )  =  ((x+\sqrt2)(x-\sqrt2))/(x)$