根号项a(a+1)(a+2)(a+3)+1的值

Question

我想知道是什么的平方。

Answer 1

a(a+1)(a+2)(a+3)+1
=(a+1)(a+2)(a+3)a+1
=(a²+3a+2)(a²+3a)+1
=[(a²+3a)+2](a²+3a)+1
=(a²+3a)²+2(a²+3a)+1
=(a²+3a+1)²
根号=(a²+3a+1)²
=|a²+3a+1|

Answer 2

a(a+1)(a+2)(a+3)+1
=[a(a+3)][(a+1)(a+2)]+1
=(a²+3a)[(a²+3a)+2]+1
=(a²+3a)²+2(a²+3a)+1
=(a²+3a+1)²
所以原式=|a²+3a+1|

Answer 3

a(a+1)(a+2)(a+3)+1
=[a(a+3)][(a+1)(a+2)]+1
=[a^2+3a][a^2+3a+2]+1
设[a^2+3a]=w
=w(w+2)+1
=w^2+2w+1
=(w+1)^2
=(a^2+3a+1)^2

Answer 4

a(a+1)(a+2)(a+3)+1
a(a+3)][(a+1)(a+2)]+1
=(a²+3a)[(a²+3a)+2]+1
=(a²+3a)²+2(a²+3a)+1
=(a²+3a+1)²
根号=(a²+3a+1)²
=|a²+3a+1|