应该是a(a+1)(a+2)(a+3)+1是一个完全平方式
a(a+1)(a+2)(a+3)+1
=(a^2+3a)(a^2+3a+2)+1
设a^2+3a=x
=x(x+2+1
=x^2+2x+1
=(x+1)^2
=(a^2+3a+1)^2