1954 AHSME Problem 49

The difference of the squares of two odd numbers is always divisible by 8. If a>b, and 2a+1 and 2b+1 are the odd numbers, to prove the given statement we put the difference of the squares in the form:

\begin{array}{l} \textbf{(A)}\ (2a+1)^2-(2b+1)^2\\ \textbf{(B)}\ 4a^2-4b^2+4a-4b\\ \textbf{(C)}\ 4[a(a+1)-b(b+1)]\\ \textbf{(D)}\ 4(a-b)(a+b+1)\\ \textbf{(E)}\ 4(a^2+a-b^2-b) \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.