Question

if a+b+c = 0 then a cube + b cube + c cube equals to ?

Answer 1

the answer is 0
$= (a + b + c)(a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca) \\ = 0 \times ( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca) \\ = 0$

Answer 2

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

(0)^3 = a^3 + b^3 + c^3 + 2(ab + bc + ca )

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