因式分解练习题 1-3(x-y)+3(x-y)²-(x-y)³

问题描述:

因式分解练习题 1-3(x-y)+3(x-y)²-(x-y)³

令x-y=a
原式=1-3a+3a^2-a^3
=(1-a)^3
把x-y=a带入上式得:
原式=(1-x+y)^3
((a+b)^3=a^3+3a^2b+3ab^2+b^3)

答:
将(x-y)看做一个整体变量t,则原式为:
1-3t+3t^2-t^3
=(1-t)^3
=(1-x+y)^3