Đáp án:
Giải thích các bước giải:
Có: `a + b + c + d = 0`
`<=> b + c = -( a + d )`
`<=> ( b + c )^2 = [ -( a + d )]^2`
`<=> ( b + c )^2 = ( a + d )^2`
`<=> b^2 + 2bc + c^2 = a^2 + 2ad + d^2`
`<=> b^2 + 2bc + c^2 - a^2 - 2ad - d^2 = 0`
`a^3 + b^3 + c^3 + d^3`
`= ( a^3 + d^3 ) + ( b^3 + c^3 )`
`= ( a + d )( a^2 - ad + d^2 ) + ( b + c )( b^2 - bc + c^2 )`
`= -( b + c )( a^2 - ad + d^2 ) + ( b + c )( b^2 - bc + c^2 )`
( vì `a + b + c + d = 0 => a + d = - ( b + c )` )
`= ( b + c )( b^2 - bc + c^2 - a^2 + ad - d^2 )`
`= ( b + c )( b^2 + 2bc + c^2 - a^2 - 3ad - d^2 - 3bc + 3ad )`
`= ( b + c )( 0 - 3bc + 3ad )`
`= ( b + c )( - 3bc + 3ad )`
`= 3( b + c )( ad - bc ) ( đpcm )`
