a^4+2a^3b+3a^2b^2+2ab^3+b^4

a^4+2a^3b+3a^2b^2+2ab^3+b^4=(a^4+b^4+a^2b^2)+2ab(a^2+ab+b^2)=[(a^2+b^2)^2-a^2b^2]+2ab(a^2+ab+b^2)=(a^2+ab+b^2)(a^2-ab+b^2)+)+2ab(a^2+ab+b^2)=(a^2+ab+b^2)^2