Question

(a^2+a+1)(a^2-6a+1)+12a^2 (因式分解）

要有详细的过程及运用什么方法

Answer 1

a的平方＋a＋1）（a的平方－6a＋1)+12a的平方
(a^2+a+1)(a^2-6a+1)+12a^2
=a^4-5a^3-4a^2-5a+1+12a^2
=a^4-5a^3+8a^2-5a+1
=(a^4-4a^3+6a^2-4a+1)-(a^3-2a^2+a)
=(a-1)^4-a(a-1)^2
=(a-1)^2(a^2-3a+1)
=(a-1)^2(a-3/2+√5/2)(a-3/2-√5/2)

Answer 2

(a^2+a+1)(a^2-6a+1)+12a^2
=[(a^2+1)+a][(a^2+1)-6a]+12a^2
=(a^2+1)^2-5a(a^2+1)+6a^2
=(a^2+1-2a)(a^2+1-3a)
=(a-1)^2(a^2-3a+1)