（x-y)^2+2(x-y)-8怎么化简?为什么等于（x-y+4)(x-y-2)?

来源：学生作业帮助网编辑：作业帮时间：2024/11/17 13:20:58

（x-y)^2+2(x-y)-8怎么化简?为什么等于（x-y+4)(x-y-2)?
（x-y)^2+2(x-y)-8怎么化简?为什么等于（x-y+4)(x-y-2)?

（x-y)^2+2(x-y)-8怎么化简?为什么等于（x-y+4)(x-y-2)?
（x-y)^2+2(x-y)-8
=（x-y)^2+2(x-y)+1-9
=（x-y+1)^2-3^2
=（x-y+1-3)（x-y+1+3)
=（x-y+4)(x-y-2)
其实这个可以用十字相乘法直接得出来的,把-8分解成-4×2.

因式分解，把x-y看成一个整体，
a²+2a-8 用十字相乘法分解(a+4)(a-2)
在把a=x-y代回去

（x-y)^2+2(x-y)-8
把（x-y)看成w：
w²+2w-8
=(w+4)(w-2)
=(x-y+4)(x-y-2)

（x-y)^2+2(x-y)-8
=[(x-y)+4][(x-y)-2]
=(x-y+4)(x-y-2)

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