Notation: Is $(\Delta x)^2 = \Delta x^2$?

I read this in a book and was wondering whether it's valid or not:

I thought $\Delta x^2$ would mean 'change in $x^2$', which would be quantitatively different to $(\Delta x)^2$; no?

Solution 1:

This is just notation. It is a typical convention that $\Delta x^2 = (\Delta x)^2$.

You are right that it seems ambiguous, but it is consistent in the calculus literature that I have seen that whenever they write $\Delta x^2$, they mean $(\Delta x)^2$.

Solution 2:

Yes, it is different from $(\Delta x)^2$. $(\Delta x)^2$ means square of change in $x$. Whereas $\Delta(x^2)$ means change in square of $x$.