1.试证明a(a+1)(a+2)(a+3)+1是完全平方式2.阅读杨辉三角,直接写出(a+b)的四次方、(a+b)的五次方,利用多项式乘法法则验证你的结果是否正确

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

(a^2+3a+1)^2
a^+5a^4*b+10a^3*b^2+10a^2*b^3+5a*b^4+b^5

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

4144