When $\lvert x + y\rvert > \lvert x - y\rvert$, I am aware that we can square both sides to find that $xy > 0$.
$x^2 + 2xy + y^2 > x^2 - 2xy + y^2$
$4xy > 0$
$xy > 0$
However, I'm wondering if there are other ways to arrive at $xy > 0$, because I am afraid that if I see a problem similar to this, then I won't always know that it's possible to square both sides to arrive at a simplified solution. Is there a more formulaic or step-by-step process that I can follow to arrive at $xy > 0$?