可以这样想,就是设法提出x+y+z出来,采用降次的方法,x＾3+y＾3+z＾3=x＾2(x+y+z)+y＾2(x+y+z)+z＾2(x+y+z)-x＾2(y+z)-y＾2(x+z)-z＾2(x+y)=(x＾2+y＾2+z＾2)(x+y+z)-x＾2(y+z)-y＾2(x+z)-z＾2(x+y)=(x＾2+y＾2+z＾2)(...不是m=3吗？x＾3+y＾3+z＾3这个式子等于(x＾2+y＾2+z＾2)(x+y+z)-（xy+xz+yz)(x+y+z）+3xyz

而题目是x³+y³+z³+mxyz=(x＾2+y＾2+z＾2)(x+y+z)-（xy+xz+yz)(x+y+z）+(m+3)xyz