(N+1)(N+2)(N+3)(N+4)+1
=[(N+1)(N+4)][(N+2)(N+3)]+1
=(N^2+5N+4)(N^2+5N+6)+1
=(N^2+5N)^2+10(N^2+5N)+24+1
=(N^2+5N)^2+10(N^2+5N)+25
=(N^2+5N+5)^2
(N+1)(N+2)(N+3)(N+4)+1
=[(N+1)(N+4)][(N+2)(N+3)]+1
=(N^2+5N+4)(N^2+5N+6)+1
=(N^2+5N)^2+10(N^2+5N)+24+1
=(N^2+5N)^2+10(N^2+5N)+25
=(N^2+5N+5)^2