n(n+7)-(n-3)(n-2)
=n^2+7n-(n^2-5n+6)
=n^2+7n-n^2+5n-6
=12n-6
=6(2n-1)能够被6整除.
所以:对于任意的自然数n,代数式n(n+7)-(n-3)(n-2)的值都能够被6整除.