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Difference of Odd Squares
Age 14 to 18
Challenge Level 
Here are some hints to help you with the proof:
A general odd number can be written in the form $2n+1$ where $n$ is an integer (whole number).
You will need two different (and completely unrelated) odd numbers.
Note that $2n+1$ and $2n-1$ are consecutive odd numbers, so these are not general enough to use.
Note that $2n+1$ and $2n-1$ are consecutive odd numbers, so these are not general enough to use.
The difference of two squares formula might (or might not!) be useful: $A^2-B^2 = (A+B)(A-B).$
You may be able to write the expression as $4(...)$ and so know that it is a multiple of $4$. To find another factor of $2$ consider the rest of the expression - can you prove that this must be even?
