Question

对于任意正整数n,整式（3n+1)(3n-1)-(3-n)(3+n)的值是否是十的倍数,请证明出来

Answer 1

（3n+1)(3n-1)-(3-n)(3+n)

=9n^2-1-(9-n^2)

=9n^2-1-9+n^2

=10n^2-10

=10(n^2-1)是 十的倍数