factorize (x^2-4x)(x^2-4x-1)-20

Answer 1

after expanding your expression and simplifying it, I got
x^4 - 8x^3 + 15x^2 + 4x - 20
trying a few values, I found x = 2 to be a root.
that left me with
(x-2)(x^3 - 6x^2 + 3x + 10) after a synthetic division,
and what do you know, x = 2 works here too, so we have
(x-2)(x-2)(x^2 - 4x - 5)
= (x-2)(x-2)(x-5)(x+1)