1. delta x

Is there a difference between $\displaystyle (\delta x)^2$ and $\displaystyle \delta x^2$ ?

Someone told me they are the same but i doubt it.

2. The first one means (dx) all squared, the other means delta * x^2

So unless delta is just a word meaning something, and doesn't hold a value, then they are both different.

3. To elaborate on Bruce's post, think of it like $\displaystyle -3^2$ versus $\displaystyle (-3)^2$, order of operations changes the result.

$\displaystyle \delta x^2 = \delta x^2$

$\displaystyle (\delta x)^2 = \delta ^2 x^2$

4. If $\displaystyle \delta$ is simply another variable, then your question has already been answered. However if you were asking if $\displaystyle (dx)^2=dx^2$ where dx is a differential, then this is sometimes the case. You'll find that in many books (especially physics books) a squared differential is sometimes denoted as dx^2 rather than (dx)^2, or at least that is the case in my experience. If this is the case, then they are the same.