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+2)+1 =(a²+3a+2)²-2(a²+3a+2)+1 =[(a²+3a+2)-1]² =(a²+3a+1)²是完全平方式
