2. Let $y=(17-x)(19-x)(19+x)(17+x)$, where $x$ is a real number. Find the smallest possible value of $y$.
(A) -1296
(B) -1295
(C) -1294
(D) -1293
(E) -1292
2. Answer: (A)
We have
$$
\begin{aligned}
y & =\left(17^{2}-x^{2}\right)\left(19^{2}-x^{2}\right) \\
& =x^{4}-\left(17^{2}+19^{2}\right) x^{2}+17^{2} \cdot 19^{2} \\
& =x^{4}-650 x^{2}+323^{2} \\
& =\left(x^{2}-325\right)^{2}+323^{2}-325^{2}
\end{aligned}
$$

Hence the smallest possible value of $y$ is $323^{2}-325^{2}=(-2)(648)=-1296$.