Question

分解四次因式

我知道答案，但不知道怎么做出来的。请提供过程。

Answer 1

Answer 2

丨、先去括号，然后分组。

Answer 3

t^4-4t^3m+(4m^2-1)t^2+2mt
=t(t^3-4t^2m+(4m^2-1)t+2m)
=t(t-2m)(t^2-2mt-1)

追问

第一步提取t明白，但是，第二步怎么到的第三步？

追答

=t(t^3-2t^2m-2t^2m+4m^2t-t+2m)
=t[t^2(t-2m)-2mt(t-2m)-(t-2m)]

=t(t-2m)(t^2-2mt-1)

Answer 4

(x+1)(x+2)(x+4)(x+5)-10
=(x+1)(x+5)(x+2)(x+4)-10
=(x²+6x+5)(x²+6x+8)-10
=(x²+6x)²+13(x²+6x)+40-10
=(x²+6x)²+13(x²+6x)+30
=(x²+6x+3)(x²+6x+10)