Rosalinda was the one who is right. Here is an example of an equation 

(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(x-10) = 0


that holds true when you substitute

x=1, x=2, x=3, x=4, x=5, x=6, x=7, x=8, x=9, and x=10,

for you get 0 = 0 with all 10 of those values.
However when you substitute x = 11 in it, you get

            3628800 = 0

So it's not an identity even though it works for all those 10 values of x.  To be an identity it
must work for all values of x.  x=11 is a
counterexample which proves it is not an identity.

An identity is like this:

   2x + 3 = 3(x + 1)-x 

Holds for ALL values of x, not just ten.
You cannot find a counterexample like you
can with the first one above.

Edwin