Rút gọn các biểu thức:

a) (x – 2)³ + (x + 2)³ – 6x(x + 2)(x – 2);

a) (x – 2)³ + (x + 2)³ – 6x(x + 2)(x – 2)

= [(x – 2) + (x + 2)]³ – 3(x – 2)²(x + 2) + 3(x – 2)(x + 2)² – 6x(x + 2)(x – 2)

= (x – 2 + x + 2)³ – [3(x – 2)²(x + 2) – 3(x – 2)(x + 2)²] – 6x(x + 2)(x – 2)

= (2x)³ – 3(x – 2)(x + 2)[(x – 2) – (x + 2)] – 6x(x + 2)(x – 2)

= 8x³ – 3(x – 2)(x + 2) . (–2x) – 6x(x + 2)(x – 2)

= 8x³ + 6x(x + 2)(x – 2) – 6x(x + 2)(x – 2) = 8x³.