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Factotise:
(a) x^2 + 1/x^2 - 11
(b) 4x^2 + 1/4x^2 + 1

Dear student,
Kindly refer the link for answer to your first query:
https://www.meritnation.com/ask-answer/question/factorisationx2-1-x2-11/algebraic-expressions/10357459 

And here is the solution for second query:
4x2+14x2+1=2x2+12x2+1=2x2+12x2+2-1=2x2+12x2+2×2x×12x-1=2x+12x2-12                              {since a2+b2+2ab=a+b2}=2x+12x+12x+12x-1         {since a2-b2=a+ba-b}

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solution of this question is :- a) x^2 +1/x^2 -11 = (x)^2 + (1/x)^2 -2 -9 = (x - 1/x)^2 - (3)^2 [by using (x - 1/x)^2 = x^2 +1/x^2 - 2] = (x - 1/x +3)(x - 1/x - 3) [by using (x+y)(x-y)=x^2 - y^2] b)4x^2 + 1/4x^2 + 1 = (2x)^2 +(1/2x)^2 + 2 - 1 =(2x + 1/2x)^2 - 1 =(2x + 1/2x +1)(2x + 1/2x - 1)
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