(x^3+y^3+z^3-3xyz)怎么因式分解?急

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(x^3+y^3+z^3-3xyz)怎么因式分解?急(x^3+y^3+z^3-3xyz)怎么因式分解?急(x^3+y^3+z^3-3xyz)怎么因式分解?急x³+y³+z³

(x^3+y^3+z^3-3xyz)怎么因式分解?急
(x^3+y^3+z^3-3xyz)怎么因式分解?

(x^3+y^3+z^3-3xyz)怎么因式分解?急
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)