Question

which identity we should use in (x)whole square -1

Answer 1

x²-1=(x-1)(x+1)

Identity: a²-b²=(a-b)(a+b)

Answer 2

The expression given by you is: $x^{2}-1$, if I am not wrong. 
If we factorise this expression, then we get
$x^{2}-1 = x^{2} - 1^{2} = (x+1)(x-1)$
And, this is similar to this identity: $a^{2}-b^{2} = (a+b)(a-b)$

∴ The identity $a^{2}-b^{2} = (a+b)(a-b)$ should be used. 

Hope this may help you. 

If you have any doubt, then you can ask me in the comments.