换元：令t=x^2+3x+3
原式=(x^2+2x+3)(x^2+4x+3)-3x^2
=(t-x)(t+x)-3x^2
=t^2-x^2-3x^2
=t^2-4x^2
=t^2-(2x)^2
=(t-2x)(t+2x)
=(x^2+x+3)(x^2+5x+3)
如仍有疑惑,欢迎追问.