As far as I have grasped the concept is that if we are given the expression

$$y[n]=(2x[n]-x^2[n])^2\,,$$

it is a memory less system because even if we give negative values of $n$, we still get the overall result in the positive sign, right?

And this expression is memory system because we get the negative answer for negative values of $n$, right?

$$y[n]=(2x[n]-x^2[n])\,.$$