I always had this confusion of when I need to apply the negative sign in the calculation. I understand that $(-1)^2 = 1$ however why isn't $-1^2 = 1$?
When we write $-x^2$, it means we square $x$ first, then take the negative of this. That is, $$-x^2 = -\left(x^2\right).$$ So $$-1^2 = -\left(1^2\right)=-1.$$ (And thus $-x^2$ means something different to $(-x)^2$.)
Unary minus has lower precedence than elevation to a power.
As it is already in the previous answers:
$(-x)^2\neq-x^2$ To avoid confusion, it is better to use parentheses. $-x^2=-(x^2)$