Question

分解因式(x-2)(x-4)(x-6)(x-8)+16=

讲解一下过程，O(∩_∩)O谢谢

Answer 1

原式=[(x-2)(x-8)][(x-4)(x-6)]+16
=[(x²-10x)+16][(x²-10x)+24]+16
=(x²-10x)²+40(x²-10x)+384+16
=(x²-10x)²+40(x²-10x)+400
=(x²-10x+20)²

追问

这一步怎样得来的？(x²-10x)²+40(x²-10x)+384+16

追答

乘出来
采纳吧

Answer 2

(x-2)(x-4)(x-6)(x-8)+16=（x²-10x+16)(x²-10x+48)+16
=(x²-10x)²+64(x²-10x)+768+16
=(x²-10x)²+64(x²-10x)+784
=(x²-10x+49)(x²-10x+16)
=(x²-10x+49)(x-2)(x-8)

Answer 3

Answer 4

=【(x-2)(x-8)】【(x-4)(x-6)】+16
=(x²-10x+16)(x²-10x+24)+16
=(x²-10x)²+40(x²-10x)+384+16
=(x²-10x)²+40(x²-10x)+400
=(x²-10x+20)²