Question

（x-1)(x-2)(x-3)(x-4)怎么算，要用简便的方法来算

要用简便的方法来算

Answer 1

（x-1）(x-4)=(x^2-5x+4)
(x-2)(x-3)=(x^2-5x+6)
所以原式=（x^2-5x+5）^2-1
=x^4-10x^3+35x^2-50x+24

Answer 2

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