1958 AHSME Problem 23

If, in the expression x^2 - 3, x increases or decreases by a positive amount of a, the expression changes by an amount:

\begin{array}{l} \textbf{(A)}\ {\pm 2ax + a^2}\qquad \textbf{(B)}\ {2ax \pm a^2}\qquad \textbf{(C)}\ {\pm a^2 - 3} \qquad \textbf{(D)}\ {(x + a)^2 - 3}\qquad\\ \textbf{(E)}\ {(x - a)^2 - 3} \end{array}

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