a(b^3-c^3)+b(c^3-a^3)+c(a^3-b^3)
=a(b^3-c^3)+b(c^3-a^3) - c[ (b^3-c^3)+(c^3-a^3)]
=(a-c)(b^3-c^3)+(b-c)(c^3-a^3)
立方差公式=(a-c)(b-c)(b^2+bc+c^2)+(b-c)(c-a)(c^2+ac+a^2)
=(a-c)(b-c)[b^2+bc+c^2-(c^2+ac+a^2)]
=(a-c)(b-c)[(b^2-a^2)+(bc-ac)]
=(a-c)(b-c)(b-a)(a+b+c)