2a(a+1)^2+a^4-a^2+1
=2a(a^2+2a+1)+a^4-a^2+1
=2a^3+4a^2+2a+a^4-a^2+1
=a^4+2a^3+3a^2+2a+1
=a^2(a^2+3)+2a(a^2+2)+1