2n(n^2+2n+1)-2n^2(n+1)
=2n^3+4n^2+2n-2n^3-2n^2
=2n^2+2n
=2n(n+1)
n和n+1是相邻的自然数,所以一奇一偶
所以n(n+1)能被2整除
所以2n(n+1)能被4整除
所以整式2n(n^2+2n+1)-2n^2(n+1)可被4整除.