因式分解x^3-y^3-8z^3-6xyz
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x^3-y^3-8z^3-6xyz
=(x-y)(x^2+xy+y^2)-8z^3-6xyz
=(x-y)[(x-y)^2+3xy]-8z^3-6xyz
=(x-y)^3+3xy(x-y)-8z^3-6xyz
=(x-y)^3-(-2z)^3+3xy(x-y)-6xyz
=(x-y-2z)[(x-y)^2+2z(x-y)+4z^2]+3xy(x-y-2z)
=(x-y-2z)[(x-y)^2+2z(x-y)+4z^2+3xy]
=(x-y-2z)(x^2+xy+y^2+2zx-2zy+4z^2)
=(x-y)(x^2+xy+y^2)-8z^3-6xyz
=(x-y)[(x-y)^2+3xy]-8z^3-6xyz
=(x-y)^3+3xy(x-y)-8z^3-6xyz
=(x-y)^3-(-2z)^3+3xy(x-y)-6xyz
=(x-y-2z)[(x-y)^2+2z(x-y)+4z^2]+3xy(x-y-2z)
=(x-y-2z)[(x-y)^2+2z(x-y)+4z^2+3xy]
=(x-y-2z)(x^2+xy+y^2+2zx-2zy+4z^2)
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