因式分解:(x+y-2z)立方+(y+z-2x)立方+(z+x-2z)立方
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因式分解:(x+y-2z)立方+(y+z-2x)立方+(z+x-2z)立方
最后那个括号 有无打错?
第三个括号改下的话.
(x+y-2z)^3+(y+z-2x)^3+(z+x-2y)^3
=[(x+y-2z)+(y+z-2x)][(x+y-2z)^2-(x+y-2z)(y+z-2x)+(y+z-2x)^2]+(z+x-2y)^3
=(2y-x-z){(x+y-2z)[(x+y-2z)-(y+z-2x)]+(y+z-2x)^2}+(z+x-2y)^3
=(2y-x-z)[(x+y-2z)(3x-3z)+(y+z-2x)^2]-(2y-x-z)^3
=(2y-x-z)[(x+y-2z)(3x-3z)+(y+z-2x)^2-(2y-x-z)^2]
=(2y-x-z){3(x+y-2z)(x-z)+[(y+z-2x)+(2y-x-z)][(y+z-2x)-(2y-x-z)]}
=(2y-x-z)[3(x+y-2z)(x-z)+(3y-3x)(-y+2z-x)]
=(2y-x-z)[3(x+y-2z)(x-z)-3(y-x)(x+y-2z)]
=3(x+y-2z)(2y-x-z)[(x-z)-(y-x)]
=3(x+y-2z)(2y-x-z)(2x-z-y)
第三个括号改下的话.
(x+y-2z)^3+(y+z-2x)^3+(z+x-2y)^3
=[(x+y-2z)+(y+z-2x)][(x+y-2z)^2-(x+y-2z)(y+z-2x)+(y+z-2x)^2]+(z+x-2y)^3
=(2y-x-z){(x+y-2z)[(x+y-2z)-(y+z-2x)]+(y+z-2x)^2}+(z+x-2y)^3
=(2y-x-z)[(x+y-2z)(3x-3z)+(y+z-2x)^2]-(2y-x-z)^3
=(2y-x-z)[(x+y-2z)(3x-3z)+(y+z-2x)^2-(2y-x-z)^2]
=(2y-x-z){3(x+y-2z)(x-z)+[(y+z-2x)+(2y-x-z)][(y+z-2x)-(2y-x-z)]}
=(2y-x-z)[3(x+y-2z)(x-z)+(3y-3x)(-y+2z-x)]
=(2y-x-z)[3(x+y-2z)(x-z)-3(y-x)(x+y-2z)]
=3(x+y-2z)(2y-x-z)[(x-z)-(y-x)]
=3(x+y-2z)(2y-x-z)(2x-z-y)
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