x^4 + y^4 + (x + y)^4 - 2*(x^2 + x*y + y^2)^2=
x^4+y^4+x^4+y-2x^2+2x*2y=
2x^4-2x^2+y^4+y+4xy
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x^4 + y^4 + (x + y)^4 - 2*(x^2 + x*y + y^2)^2=
x^4+y^4+x^4+y-2x^2+2x*2y=
2x^4-2x^2+y^4+y+4xy