分类：教育/科学-理工学科-数学
问题：x^3+y^3+z^3
回答：　x³+y³+z³-3xyz
= [(x+y)³-3xy(x+y)] + z³-3xyz
= [(x+y)³+z³] - 3xy(x+y+z)
= [(x+y+z)³-3(x+y)z(x+y+z)] - 3xy(x+y+z)
= (x+y+z)³-3(xy+yz+zx)(x+y+z)
= (x+y+z)[(x+y+z)²-3(xy+yz+zx)]
= (x+y+z)(x²+y²+z²-xy-yz-zx)