Question

因式分解：x³+y³+z³-3xyz

（右上角的立方可能有点小，前三个项都是立方。）
另外解题步骤请尽量详细些。谢谢。

Answer 1

x³+y³+z³-3xyz
=x³+3x²y+3xy²+y³+z³-3x²y-3xy²-3xyz
=(x+y)³+z³-3xy(x+y+z)
=(x+y+z)(x²+2xy+y²-xz-yz-3xy)
=(x+y+z)(x²+y²+z²-xy-yz-xz)

Answer 2

﹙a＋b＋c﹚﹙a²＋b²＋c²－ab－ac－bc﹚