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x3(y-z)+y3(z-x)+z3(x-y)

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/11 19:10:14
x3(y-z)+y3(z-x)+z3(x-y)
x3(y-z)+y3(z-x)+z3(x-y)
=x3(y-z)+y3(z-x)-z3(y-z)-z3(z-x)
=(x3-z3)(y-z)+(y3-z3)(z-x)
=(x-z)(y-z)(x2+xz+z2)-(x-z)(y-z)(y2+yz+z2
=(x-z)(y-z)(x2+xz-y2-yz)
=(x-z)(y-z)[(x-y)(x+y)+(x-y)z]
=(x-y)(x-z)(y-z)(x+y+z).