GMAT Data Sufficiency (DS) | Re: Is |x|*y - x*|y| > x*y, where x and y are non-zero integers

Hello Friends, i got this question right but i couldn't corelate my method with anything given here
(i did similar to what Vyshak's did but without some key steps i think it is difficult to understand). If i am wrong PLEASE correct me. Here itgoes

[1] y <0
[1.a] y < 0 and x > 0
|x|*y - x*|y| = x*(-y) -x*[-(-y)] = -xy - xy = -2xy
x*y = x*(-y) = -xy
-2xy >| -xy

[1.b] y < 0 and x < 0
|x|*y - x*|y| =[-(-x)] *(-y) -(-x)*[-(-y)] = -xy + xy = 0
x*y = (-x)*(-y) = xy
0 >| xy
Thus 1Suff
[2] x*y > 0 =>
...

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