what's the difference between (F(x))^2 and F^2(x) ?

Step-by-step explanation:
I am sorry to say so, but the other answer is rubbish.
there is no difference.
both mean the same thing : f(x) × f(x).
f(f(x)) is exactly what that expresses (f of f(x)).
another way of writing for this would be (f○f)(x).
but never ever f²(x).
please ignore the other answer.