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

 Nov 1, 2017
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 (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 !!!!

 

 

cool cool cool

 Nov 1, 2017

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