a^4+3ab^2+b^4-a^3b-3a^2b-ab^3
=(a^4-a^3b)+(3ab^2-3a^2b)+(b^4-ab^3)
=a^3(a-b)-3ab(a-b)-b^3(a-b)
=a^3-3ab-b3
=(a^3-b^3)-3ab
=(a-b)(a^2+ab+b^2)-3ab
=a^2+ab+b^2-3ab
=a^2-2ab+b^2
=(a-b)^2
=1