factorize:(x+1)(x+2)(x+3)(x+6)-3x^2

= (x+2)(x+3) ( x+ 1)(x+6) - 3x^2
= (x^2 + 5x + 6)(x^2 + 7x + 6) - 3x^2 ( we take the product such that constants in both products are same)

let x^2 + 6x + 6 = z

so we get ( z- x)(z + x) - 3x^2
= z^2 - x^2 - 3x^2
= z^2 - 4x^2
= (z+2x)(z-2x)
= (x^2 +8x + 6)(x^2+ 4x + 6)
cannot be factored further.