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