急~高手救我~因式分解下列各式： 一.a²(b-c)+b²(c-a)+c²(a-b) 二.（x-6)(x-3)(x+2)(x+4)-84x²?

一.
a²(b - c) + b²(c - a) + c²(a - b)
= a²b - ca² + b²c - ab² + c²(a - b)
= (a²b - ab²) + (-ca² + b²c) + c²(a - b)
= ab(a - b) - c(a² - b²) + c²(a - b)
= ab(a - b) - c(a + b)(a - b) + c²(a - b)
= (a - b)[ab - c(a + b) + c²]
= (a - b)[ab - ca - bc + c²]
= (a - b)[(ab - ca) - (bc - c²)]
= (a - b)[a(b - c) - c(b - c)]
= (a - b)(b - c)(a - c)

答案可寫成：
(b - a)(c - b)(a - c)， (a - b)(c - b)(c - a) 或 (b - a)(c - b)(a - c)

====
二.
原式
= (x - 6)(x - 3)(x + 2)(x + 4) - 84x²
= [(x - 6)(x + 2)][(x - 3)(x + 4)] - 84x²
= (x² - 12 - 4x)(x² - 12 + x) - 84x²
= [(x² - 12) - 4x][(x² - 12) + x] - 84x²

令 y = x² - 12
原式
= (y - 4x)(y + x) - 84x²
= (y² + xy - 4xy - 4x²) - 84x²
= y² - 3xy - 88x²
= (y - 11x)(y + 8x)
= [(x² - 12) - 11x][(x² - 12) + 8x]
= (x² - 11x - 12)(x² + 8x - 12)
= (x + 1)(x - 12)(x² + 8x - 12)

若接受無理因式，
則 x² + 8x - 12 可因式分解成 (x + 4 + 2√7)(x + 4 - 2√7)