Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a + b + c + d = 0 \Rightarrow a + b = - \left( {c + d} \right)\\
{a^3} + {b^3} + {c^3} + {d^3}\\
= \left( {{a^3} + 3{a^2}b + 3a{b^2} + {b^3}} \right) + \left( {{c^3} + 3{c^2}d + 3c{d^2} + {d^3}} \right) - \left( {3{a^2}b + 3a{b^2} + 3{c^2}d + 3c{d^2}} \right)\\
= {\left( {a + b} \right)^3} + {\left( {c + d} \right)^3} - 3ab\left( {a + b} \right) - 3cd\left( {c + d} \right)\\
= {\left[ { - \left( {c + d} \right)} \right]^3} + {\left( {c + d} \right)^3} - 3ab.\left[ { - \left( {c + d} \right)} \right] - 3cd\left( {c + d} \right)\\
= - {\left( {c + d} \right)^3} + {\left( {c + d} \right)^3} + 3ab\left( {c + d} \right) - 3cd\left( {c + d} \right)\\
= 3ab\left( {c + d} \right) - 3cd\left( {c + d} \right)\\
= 3.\left( {c + d} \right)\left( {ab - cd} \right)
\end{array}\)
