因式分解考考你

1.a^12 - b^12
= (a^6 - b^6)(a^6 + b^6)
= (a^2 - b^2)(a^4 + a^2b^2 + b^4)(a^2 + b^2)(a^4 - a^2b^2 + b^4)
= (a - b)(a + b)(a^4 + 2a^2b^2 + b^4 - a^b^2)(a^2 + b^2)(a^4 + 2a^2b^2 + b^4 - 3a^2b^2)
= (a - b)(a + b)[(a^2 + b^2) - (ab)^2](a^2 + b^2)[(a^2 + b^2)^2 - (√3ab)^2]
= (a - b)(a + b)(a^2 + ab + b^2)(a^2 - ab + b^2)(a^2 + b^2)(a^2 + √3ab + b^2)(a^2 - √3ab + b^2)

2.x^3 + 4x^2 + x - 6
= x^3 - x^2 + 5x^2 - 5x + 6x - 6
= x^2(x - 1) + 5x(x - 1) + 6(x - 1)
= (x - 1)(x^2 + 5x + 6)
= (x - 1)(x^2 + 2x + 3x + 6)
= (x - 1)[x(x + 2) + 3(x + 2)]
= (x - 1)(x + 2)(x + 3)
3.x^3 + x^2 - 12
= x^3 - 2x^2 + 3x^2 - 6x + 6x - 12
= x^2(x - 2) + 3x(x - 2) + 6(x - 2)
= (x - 2)(x^2 + 3x + 6)