Prove algebraically that (2n+3)^2 - (2n-3)^2 is a multiple of 8, for all positive integer values of n

 (2n+3)^2 - (2n-3)^2

Factor

[ (2n +3)  - (2n - 3) ] [ (2n + 3) + (2n - 3) ]  =

[  6 ]  [  4n ]  =

24n  =

8 [ 3n ]    so.....this is a multiple of 8 !!!!