(x+y)^2+9(x-y)^2-6(x^2-y^2)
=(x+y)^2-6(x^2-y^2)+9(x-y)^2
=(x+y)^2-6(x-y)(x+y)+9(x-y)^2
=[(x+y)-3(x-y)]^2
=(x+y-3x+3y)^2
=(4y-2x)^2
=(2x-4y)^2
=4(x-2y)^2