SOLUTION: Write an algebraic expression that proves the difference of the square of any two odd numbers must be divisible by 8.

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Write an algebraic expression that proves the difference of the square of any two odd numbers must be divisible by 8.      Log On


   

Question 146745: Write an algebraic expression that proves the difference of the square of any two odd numbers must be divisible by 8.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%28n%2B2%29%5E2+-+n%5E2+=+n%5E2+%2B+4n+%2B4+-n%5E2
= 4n + 4
=4(n + 1)
Since n is odd, n+1 is even, meaning it has at least one factor of 2.
4 times that has to be divisible by 8, as it adds 2 more factors of 2.