Cho a + b + c = 0. Chứng minh: a³ + b³ + c³ = 3abc.

a + b + c = 0

Þ (a + b + c)³ = 0

Û a³ + b³ + c³ + 3a²b + 3ab² + 3b²c + 3bc² + 3a²c + 3ac² + 6abc = 0

Û a³ + b³ + c³ + (3a²b + 3ab² + 3abc) + (3b²c + 3bc² + 3abc) + (3a²c + 3ac² + 3abc) − 3abc = 0

Û a³ + b³ + c³ + 3ab(a + b + c) + 3bc(a + b + c) + 3ac(a + b + c) = 3abc

Do a + b + c = 0

Þ a³ + b³ + c³ = 3abc (đpcm)