2. Given that $a$ and $b$ are two different positive integers. Ask:
$$
\begin{array}{l}
a(a+2), a b, a(b+2), (a+2) b, \\
(a+2)(b+2), b(b+2)
\end{array}
$$

Among these six numbers, what is the maximum number of perfect squares?
2. At most two numbers are perfect squares (such as $a=2, b=16$). Notice that,
$$
\begin{array}{l}
a(a+2)=(a+1)^{2}-1, \\
b(b+2)=(b+1)^{2}-1
\end{array}
$$

cannot be perfect squares;
$$
a b \cdot a(b+2)=a^{2}\left(b^{2}+2 b\right)
$$

is not a perfect square, so at most one of $a b$ and $a(b+2)$ is a perfect square.

Similarly, at most one of $(a+2) b$ and $(a+2)(b+2)$ is a perfect square.
Thus, at most two numbers are perfect squares.