Question

If a +b + c = 0, then what is a³ + b³ + c³ equal to?

Answer 1

wait a minute
${a}^{3} + b {}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac)$
but a +b + c is 0 so
${a}^{3} + {b}^{3} + {c}^{3} - 3abc \: = (0)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac) \\ = {a}^{3} + {b}^{3} + {c}^{3} - 3abc = 0 \\ {a}^{3} + {b}^{3} + {c}^{3} = 3abc$
hope it helps