if a+b+c=0 then, a cube + b cube + c cube
it is given that a + b + c = 0
we know that-
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
a3 + b3 + c3 - 3abc = (0)(a2 + b2 + c2 - ab - bc - ac)
a3 + b3 + c3 - 3abc = 0
a3 + b3 + c3 = 3abc
if a+b+c=0 then, a cube + b cube + c cube
it is given that a + b + c = 0
we know that-
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
a3 + b3 + c3 - 3abc = (0)(a2 + b2 + c2 - ab - bc - ac)
a3 + b3 + c3 - 3abc = 0
a3 + b3 + c3 = 3abc