n²+n²*(n+1)²+(n+1)²=
=n²+[n(n+1)]²+n²+2n+1
=[n(n+1)]²+n²+n²+2n+1
=(n²+n)²+2n²+2n+1
=(n²+n)²+2(n²+n)+1
=(n²+n+1)²
计算2008²+2008²*2009²+2009²
这里n=2008
2008²+2008²*2009²+2009²
=(2008²+2008+1)²
n²+n²*(n+1)²+(n+1)²=
=n²+[n(n+1)]²+n²+2n+1
=[n(n+1)]²+n²+n²+2n+1
=(n²+n)²+2n²+2n+1
=(n²+n)²+2(n²+n)+1
=(n²+n+1)²
计算2008²+2008²*2009²+2009²
这里n=2008
2008²+2008²*2009²+2009²
=(2008²+2008+1)²