The ASUS R704A 17" laptop is the same as an X75A-104A.

TL;DR: The big take aways are:

1. I've opened my R704A-RB31 and yes there is a single empty DIMM slot.
2. The Asus R704A is the same as the Asus X75A-Z104.

I bought this laptop / notebook at Fry's on a great sale ($378), hoping to upgrade the RAM to 8GB, as it comes with 4GB.

Dilemma:
Both Fry's and Newegg web sites said there was one empty DIMM slot allowing upto 8GB.  Good.

Many, many other sites on the internet including microcenter indicated there was one 4GB DIMM soldered to the M/B and that was it.  No upgrading.  Bad.

The ASUS website had no information on the R704A.  No specs.  No downloads.  No nothing.   Ack.

Several weeks later, the ASUS support site still had limited information but I was able to download a user manual, which was labelled X75A-104A, which is another 17" laptop ASUS makes.  And this model has full specs/info on the Asus support site.  And it says there is a single DIMM slot allowing upto 8GB of RAM.  Here's a link to all  manuals and documentation  for this laptop.  Choose other tabs too.

To get at the RAM and hard drive, unscrew and remove the two screws holding the big panel which covers the front half of the bottom.  Pull the plastic toward the front and it should just slide off.

Armed with this knowledge I finally opened the laptop and indeed there is an unfilled user accessible memory slot.