因式分解(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3kkkkkkkkk_数学解答

因式分解(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3
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人气：382 ℃　时间：2020-04-13 11:42:17

解答

(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=((x+y+z)^3-(y+z-x)^3)-((z+x-y)^3+(x+y-z)^3)=(x+y+z-y-z+x)((x+y+z)^2+(x+y+z)(y+z-x)+(y+z-x)^2)-(z+x-y+x-z+y)((z+x-y)^2-(z+x-y)(x+y-z)+(x+y-z)^2)=2x((x+y+z)^2+(x+...