证明:(y+z-2x)^3+(z+x-2y)^3+(x+y-2z)^3=3(y+z-2x)(z+x-2y)(x+y-2z)

问题描述:

证明:(y+z-2x)^3+(z+x-2y)^3+(x+y-2z)^3=3(y+z-2x)(z+x-2y)(x+y-2z)
注意:是证明不是解答!

证:(y+z-2x)³+(z+x-2y)³+(x+y-2z)³=[(y+z-2x)³+(z+x-2y)³]+(x+y-2z)³ /前面两项运用立方和公式=[(y+z-2x)+(z+x-2y)][(y+z-2x)²-(y+z-2x)(z+x-2y)+(z+x-2y)²]+(x+y-2z)...