Question

x的立方+y的立方+z的立方-3xyz 因式分解,

Answer 1

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)