What if I run an ethernet cable from the Extreme to the Express and program the Express to extend the network?
This would be the ideal way to extend a wireless network because the Ethernet connection will maintain maximum bandwidth for the network. The Express, which is connected via Ethernet from the AirPort Extreme could then be configured to allow the network to be extended using wireless only.
Careful...if you connect the Express to the Extreme using Ethernet, you will not configure the Express to "extend a wireless network" as you might think. Instead, the Express would be configured to "Create a wireless network using the exact same wireless network name, security and password as the AirPort Extreme network. In addition, the Express would need to be configured in Bridge Mode for this type of setup.
The advantage of using Ethernet is two fold:
1) It provides maximum bandwidth for the network
2) It allows you to locate the AirPort Express exactly where it is needed to provide more coverage. With the "extend" setup using wireless only, the Express is normally located about half the distance from the "hub" to the area that needs more wireless coverage