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 !!!!