Question

∵a+b+c=0 ∴a的立方+b的立方+c的立方=3abc 是怎么推得

Answer 1

a^3+b^3+c^3-3abc

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

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

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

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

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