xy(x2-y2)+yz(y2-z2)+zx(z2-x2) 因式分解 对称多项式
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xy(x2-y2)+yz(y2-z2)+zx(z2-x2)
=x^3y-xy^3+y^3z-yz^3+z^3x-zx^3
=(y-z)x^3-(x-z)y^3+(x-y)z^3
=(y-z)x^3-(x-y+y-z)y^3+(x-y)z^3
=(y-z)(x^3-y^3)+(x-y)(z^3-y^3)
=(x-y)(y-z)(x^2+xy+y^2-z^2-zy-y^2)
=(x-y)(y-z)(x^2-z^2+xy-zy)
=(x-y)(y-z)(x-z)(x+y+z)
=x^3y-xy^3+y^3z-yz^3+z^3x-zx^3
=(y-z)x^3-(x-z)y^3+(x-y)z^3
=(y-z)x^3-(x-y+y-z)y^3+(x-y)z^3
=(y-z)(x^3-y^3)+(x-y)(z^3-y^3)
=(x-y)(y-z)(x^2+xy+y^2-z^2-zy-y^2)
=(x-y)(y-z)(x^2-z^2+xy-zy)
=(x-y)(y-z)(x-z)(x+y+z)
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