20. For any fixed value of $x$, which of the following four expressions has the largest value?
$$
\begin{array}{llll}
(x+1)(x-1) & \left(x+\frac{1}{2}\right)\left(x-\frac{1}{2}\right) & \left(x+\frac{1}{3}\right)\left(x-\frac{1}{3}\right) & \left(x+\frac{1}{4}\right)\left(x-\frac{1}{4}\right) \\
\text { A }(x+1)(x-1) & \text { B }\left(x+\frac{1}{2}\right)\left(x-\frac{1}{2}\right) & \text { C }\left(x+\frac{1}{3}\right)\left(x-\frac{1}{3}\right) & \mathrm{D}\left(x+\frac{1}{4}\right)\left(x-\frac{1}{4}\right)
\end{array}
$$

E it depends on the value of $x$
20. D The first four expressions expand to $x^{2}-1 ; x^{2}-\frac{1}{4} ; x^{2}-\frac{1}{9} ; x^{2}-\frac{1}{16}$ respectively. Note that $\frac{1}{16}<\frac{1}{9}<\frac{1}{4}<1$. Therefore the least value is $x^{2}-\frac{1}{16}$, that is $\left(x+\frac{1}{4}\right)\left(x-\frac{1}{4}\right)$. This result is irrespective of the value of $x$.