Đáp án:
Giải thích các bước giải:
a) ( a + b)³ + ( a - b)³ - 6a²b
= ( a + b + a - b)[( a + b)² -
( a + b)( a - b) + ( a - b)² ]- 6a²b
= 2a( a² + 2ab + b² - a² + b² + a²
- 2ab + b²) - 6a²b
= 2a( a² + 3b²) - 6a²b
= 2a³ + 6ab² - 6a²b
b) ( a + b)³ - ( a - b)³ - 6a²b
= ( a + b - a + b)[( a + b)² +
( a - b)( a + b) + ( a - b)² ] - 6a²b
= 2b( a² + 2ab + b² + a² - b² + a²
- 2ab + b²) - 6a²b
= 2b( 3a² + b² ) - 6a²b
= 2b³ + 6a²b - 6a²b
= 2b³
c) ( x +2)³ + ( x - 2)³ - 2x(x² + 12)
= ( x + 2 + x - 2)[( x + 2)² - ( x + 2)
( x - 2) + ( x - 2)² ] - 2x( x² + 12)
= 2x( x² + 4x + 4 - x² + 4 + x² - 4x + 4] - 2x³ - 24x
= 2x(x² + 12) - 2x³ - 24
= 2x³ + 24x - 2x³ - 24x
= 0
d) (x + 1)³ - (x + 1)³ + 6(x + 1)(x -1)
=( x +1 - x - 1)[ ( x +1)² + ( x + 1)
( x + 1) + ( x + 1)² ] + 6( x² - 1)
= 0.[( x + 1)² + ( x +1)² + ( x +1)² ] + 6x² - 6
= 0 + 6x² - 6
= 6x² - 6
