3xy-{(3y-x)(2x-y)-[4xy-x(2x-3y)]-3y(x-y)}=
3xy-{(3y-x)(2x-y)-[4xy-x(2x-3y)]-3y(x-y)}=
* "3xy-{(3y-x)(2x-y)-[4xy-x(2x-3y)]-3y(x-y)}" ≡
≡ 3*x*y - ((3*y - x)*(2*x - y) - (4*x*y - x*(2*x - 3*y)) - 3*y*(x - y)) =
= 3*x*y - (3*y*(2*x - y) - (x*2*x - x*y) - (4*x*y - (x*2*x - x*3*y)) - (3*y*x - 3*y*y)) =
= 3*x*y - (3*y*2*x - 3*y*y - x*2*x + x*y - 4*x*y + x*2*x - x*3*y - 3*y*x + 3*y*y) =
= 3*x*y - 3*y*2*x + 3*y*y + x*2*x - x*y + 4*x*y - x*2*x + x*3*y + 3*y*x - 3*y*y =
= 3*x*y - 6*x*y + 3*y^2 + 2*x^2 - x*y + 4*x*y - 2*x^2 + 3*x*y + 3*x*y - 3*y^2 =
= 2*x^2 - 2*x^2 + 3*x*y - 6*x*y - x*y + 4*x*y + 3*x*y + 3*x*y + 3*y^2 - 3*y^2 =
= (2 - 2)*x^2 + (3 - 6 - 1 + 4 + 3 + 3)*x*y + (3 - 3)*y^2 =
= 0*x^2 + 6*x*y + 0*y^2 =
= 6*x*y
http://www.wolframalpha.com/input?i=simplify%283xy-%7B%283y-x%29%282x-y%29-%5B4xy-x%282x-3y%29%5D-3y%28x-y%29%7D%29