2、Use $\mathbf{R} 、 \mathbf{G} 、 \mathbf{B}$ three colors to color the following $2 \times 5$ table, requiring that two cells sharing a common edge must be colored differently. Question: How many different coloring methods are there in total?
【Analysis】Consider 2 rows and $a$ columns, let 2 rows and $a$ columns have $b$ different coloring methods, and then add 1 column to its right.
For each of the $b$ coloring methods, consider how many different coloring methods there are for the column to its right.
Obviously, if the colors of cells 1 and 2 are different, and the color of cell 3 is different from that of cell 1, if cell 3 is the same color as cell 2, then cell 4 has 2 coloring methods; if cell 3 is a different color from cell 2, then cell 4 has 1 coloring method. Therefore, the $(a+1)$-th column has $1 \times 2 + 1 \times 1 = 3$ coloring methods, so 2 rows and $(a+1)$ columns have $3b$ different coloring methods.
2 rows and 1 column have $3 \times 2 = 6$ coloring methods.
Therefore, 2 rows and 5 columns have $6 \times 3 \times 3 \times 3 \times 3 = 486$ coloring methods.