(x-1)(x-2)(x-3)(x-4)
=[(x-1)(x-4)][(x-2)(x-3)]
=(x²-5x+4)(x²-5x+6)
=(x²-5x+5)²-1
=x4+25x²+25-10x3+10x²-50x-1
=x4-10x3+35x²-50x+24
(x-1)(x-2)(x-3)(x-4)
=[(x-1)(x-4)][(x-2)(x-3)]
=(x²-5x+4)(x²-5x+6)
=(x²-5x+5)²-1
=x4+25x²+25-10x3+10x²-50x-1
=x4-10x3+35x²-50x+24