(x+1)(x+2)(x+3)(x+6)-3x^2
=[(x+1)(x+6)][(x+2)(x+3)]-3x^2
=(x^2+7x+6)(x^2+5x+6)-3x^2
=(x^2+6x+6+x)(x^2+6x+6-x)-3x^2
=(x^2+6x+6)^2-4x^2
=(x^2+8x+6)(x^2+4x+6)