因式分解 (a-1)(a+1)(a+3)(a+5)+16

分类: 作业答案 • 2022-02-05 16:54:02

问题描述：

答

(a-1)(a+1)(a+3)(a+5)+16
=[(a-1)(a+5)][(a+1)(a+3)]+16
=(a^2+4a-5)(a^2+4a+3)+16
=(a^2+4a)^2-2(a^2+4a)-15+16
=(a^2+4a-1)^2
=(a-√5+2)^2(a+√5+2)^2