Question

几道因式分解

(a^2+5a+4)(a^2+5a+10)+9

a^5-4a^3+a-2

6x^2-13xy+6y^2+8xz-2yz-8z^2

(x^2-3x)^2+2(3x-x^2)-8

求过程，谢谢
第一个且对的给分

Answer 1

(a^2+5a+4)(a^2+5a+10)+9
=(a^2+5a+7-3)(a^2+5a+7+3)+9
=(a^2+5a+7)^2

a^5-4a^3+a-2
=a^3(a+2)(a-2)+(a-2)
=(a-2)(a^4+2a^3+1)
=(a-2)(a^4+2a^3+a^2-a^2+1)
=(a-2)[a^2(a+1)^2-(a+1)(a-1)]
=(a-2)(a+1)(a^3+a^2-a+1)

(x^2-3x)^2+2(3x-x^2)-8
=(x^2-3x)^2-2(x^2-3x)-8
=(x^2-3x-4)(x^2-3x+2)
=(x-4)(x+1)(x-1)(x-2)