a(b+c)^2+b(c+a)^2+c(a+b)^2-4abc=
=a(b+c)^2+b(c^2+2ac+a^2)+c(a^2+2ab+b^2)-4abc=
=a(b+c)^2+(bc^2+2abc+ba^2)+(ca^2+2abc+cb^2)-4abc=
=a(b+c)^2+(bc^2+ba^2+ca^2+cb^2)=
=a(b+c)^2+a^2(b+c)+bc(c+b)=
=a(b+c)^2+(a^2+bc)(b+c)=
=a(b+c)(b+c)+(a^2+bc)(b+c)=
=(b+c)(a(b+c)+(a^2+bc))=
=(b+c)((ab+ac+a^2+bc))=
=(b+c)((a^2+ab)+(bc+ac))=
=(b+c)((a(a+b)+c(a+b))=
=(b+c)(a+b)(a+c)