SOLUTION: Prove that the difference of the squares of two consecutive odd numbers is a multiple of 8. Note that an even number can be written as 2n.

SOLUTION: Prove that the difference of the squares of two consecutive odd numbers is a multiple of 8. Note that an even number can be written as 2n.

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Question 1051281: Prove that the difference of the squares of two consecutive odd numbers is a multiple of 8. Note that an even number can be written as 2n.

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Let the odd numbers be 2n-1 and 2n+1 where n is an integer

(2n+1)^2 - (2n-1)^2 = (4n^2 + 4n + 1) - (4n^2 - 4n + 1) = 8n

8n is a multiple of 8, so we are done.
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