Are speaker wire output negative posts on receiver common-grounded?
That Sony does not have a dedicated sub woofer output so you will need a sub-woofer that will pass through the sound to your  left and right speakers. Some subs only except a sub channel input and do not pass through left and right channels, many will except and pass along the right and left channels to the speakers,  meaning it will have inputs for left and right and OUTPUTS for left and right. . 

As long as you wire the negative to negative  and positive to positive ( black to black and red to red ) you will be OK. 

You did not say what sub-woofer model you are getting, I am not familiar with a subs that  sub that have "negative posts joined" Can you post the model? I found the following quote on crutchfield.com for the polk PSW10 , i assume that is what you are referring to. 


  "Speaker Level Input/Output: The sub-woofer has spring clips for the
  speaker level inputs and outputs. The sub woofer's low-pass filter
  sends bass frequencies (based on the setting of the filter) to the
  sub-woofer. The speaker level inputs and outputs are shorted together,
  so the output is not crossed over. You should set you receiver's front
  speaker setting to Large."


Meaning you wire it as i stated and it passes the correct frequencies to the sub and the speakers. 

Or you can use RCA cables from the video or md/tape audio out terminals on the receiver and go into the RCA Line in, left and right on the sub-woofer and wire your speaker into the out terminals on the sub.