abc(a^3+b^3+c^3)-a^3*b^3-b^3*c^3-c^3*a^3因式分解

更新时间：2020-10-28 12:06:41 231次访问

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abc(a^3+b^3+c^3)-a^3*b^3-b^3*c^3-c^3*a^3

=abc(a^3+b^3)+abc^4-a^3b^3-c^3*(a^3+b^3)

=c(a^3+b^3)(ab-c^2)+ab(c^4-a^2b^2)

=(a^3c+b^3c)(ab-c^2)+ab(c^2+ab)(c^2-ab)

=(a^3c+b^3c)(ab-c^2)-(abc^2+a^2b^2)(ab-c^2)

=(ab-c^2)(a^3c+b^3c-abc^2-a^2b^2)

=(ab-c^2)[(a^3c-a^2b^2)+(b^3c-abc^2)]

=(ab-c^2)[a^2(ac-b^2)+bc(b^2-ac)]

=(ab-c^2)[a^2(ac-b^2)-bc(ac-b^2)]

=(ab-c^2)(ac-b^2)(a^2-bc)

=(c^2-ab)(b^2-ca)(a^2-bc)