If a + B + C = 0, what is the cubic of a + cubic of B + cubic of c-3abc!

If a + B + C = 0, what is the cubic of a + cubic of B + cubic of c-3abc!

Using cubic sum formula A ^ 3 + B ^ 3 = (a + b) (a ^ 2-AB + B ^ 2)
a^3+b^3+c^3-3abc
=[(a+b)^3-3a^2b-3ab^2]+c^3-3abc
=[(a+b)^3+c^3]-(3a^2b+3ab^2+3abc)
=(a+b+c)[(a+b)^2-(a+b)c+c^2]-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-ab-ac-bc)
∵a+b+c=0
∴ a^3+b^3+c^3-3abc=0

Elden Ring Premiere

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