x的立方+y的立方+z的立方-3xyz 因式分解,
问题描述：
x的立方+y的立方+z的立方-3xyz 因式分解,
答
x^3+y^3+z^3-3xyz =[( x+y)^3-3x^2y-3xy^2]+z^3-3xyz=[(x+y)^3+z^3]-(3x^2y+3xy^2+3xyz)=(x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z) =(x+y+z)(x^2+y^2+2xy-xz-yz+z^2)-3xy(x+y+z) =(x+y+z)(x^2+y^2+z^2-xy-xz-yz)