Question

If a + b + c = 0 , show that a 3 +b 3 +c 3 =3abc

Answer 1

a+b+c=0
⇒a+b=-c
cubing on both sides
⇒(a+b)³=-c³
⇒a³+b³+3ab(a+b)=-c³
⇒a³+b³+3ab(-c)=-c³
⇒a³+b³-3abc=-c³
⇒a³+b³+c³=3abc