If you are skilled with soldering there is a good post on here by 'ruedli' of how to do this without cutting the solder pads in half.
These steps are for those of us that are familiar, but are not super skilled with soldering. I have done basic soldering but the connections on these strips were too close together for me. I tried using a solder sucker and also the tin but couldn't do it. I had to cut in half and separate the soldering pads in order to feel comfortable that the strips would not short out due to continuity between two different lines because of either too much solder, or melting a little bit of solder accidentally onto an adjacent line.
I have seen some very good posts for those who are capable of separating the strips without cutting them. Cutting will reduce the surface area when you go back to reconnect the strips, but I was fine with that. There will still be more than enough room to add connections.
Step 1: Peel Back the Insulation and Cut
The first step is to carefully cut around the rubber insulation and then peel it back to reveal the solder pads. DO NOT CUT WHERE IT SAYS TO CUT!! I took an x-acto knife and went right down the middle of the solder pads on both sides and then carefully made perpendicular slits along each edge of the insulation in each direction in order to peel it back like a banana.
Once this is done you can now cut right down the middle of the solder pads (I just used scissors). Try to cut as close to center as possible since this method does reduce the area for adding new connections.
Again, if you are comfortable, then you can use the solder iron to heat and separate the 6 connection points.
Step 2: Separate the Solder Pads
This part is a little tedious. It will take a little time and patience. I took my x-acto knife and carefully cut down between the solder pads being careful not to cut too far, and being aware of the 6 copper strips that lead to the pads (some of them are more narrow than others).
Once this was done I slightly bent each pad opposite the next. This way when soldering I was not worried about any of the lines/pads accidentally touching when I was finished. Bend each pad the same direction, if you bend the 'C' pad forward and the 'B' pad back then follow that pattern every time. This will help when putting the pins into the housing later.
Step 3: Crimp and Solder on the Connections
I read someones post that used cat 5 cable and found that to be very convenient. It has 8 colored lines and only 6 will be needed. Also this probably goes without saying, but it would be a good idea to write down which color goes to which pad, (C, B, G, R, FW and VCC) and make note of what side of the strip you are starting on. Just nice to have a quick reference at hand when soldering these rather than looking back at a previous strip or connection.
I cut about 1 1/2 inch of cat 5 to crimp my pins to. This left me wiggle room for when I put the pins into their housing. Crimp whatever pins you decide to use for your connections before soldering. I'm sure you would have already, but just making sure, trust me it will be much easier. (Also, I get most of my stuff from Pololu.com if you don't already have male and female crimp pins and housing. Adafruit probably has them too, they shouldn't be too hard to find.)
Male on one side of course and female on the other. The first part of the strip has the plug that goes into the wall and so I started with female on the other side of that, then male followed by female on the second cut strip. (First cut strip: Wall plug on one side, female pins on other. Second cut strip: male on side to follow, female on other side, and so on.)
You could even go male on all the strip light connections and female on all the cat 5, but if you decide to do something different down the road, then you may be kinda stuck. This way you can even reconnect the strip lights back together later if you like. I would wait to crimp the cat 5 cables for when your waiting for the silicon to dry (later steps).
Now solder each crimped wire to its assigned pad. Give a little tug to each one when done to make sure of a solid connection.
Step 4: Test for NO CONTINUITY, and Then Insulate
At this point it is important to test for no continuity between any and all of the 6 lines. Use gator clips to clip to one of the voltmeter lines, then use the other line and check each solder point (not just the pins), this also checks that you made a solid connection to your pin wire. If there is contact between any 2 of the 6 lines then you need to stop and check those 2 soldered connections, find out where there is contact and do not continue until this is resolved and there is no continuity between any of the 6 lines. You may have to remove one or both of those lines and re-solder, or just remove excess.
Once this is done it is time to use a little bit of silicon to seal the deal. You do not need to use a lot, I put a dab in the middle of the 6 and then used a little piece of rubber wire insulation to move and brush it around the soldered connection points, being sure to cover all exposed metal. Feel free to go up part of the wire and put a light coat around the base of the insulation there as well.
When you are done, REPEAT THE CONTINUITY TEST. Obviously this time you can only check by contacting the pins since the soldered portion is now covered. This may seem redundant but it is best to make sure nothing shifted too much when you applied the silicon. Easier to wipe off and fix while wet. Now let sit and dry, most say 24 hour cure time but 30 min to an hour and you should be good to touch.
This would be a good time to go ahead and crimp the cat 5 cables while your waiting.
Step 5: Add Pin Housing, Connect and Do One More Test
Now that the silicon is dry you can slip the housing onto the pins. I used 2x3 housing, but 1x6 would also work, just make sure the colors match up when they are going to plug into each other!! I didn't pay close enough attention the first time and I had to pull the pins back out and redo one of the first pair. No biggie.
Also, even though the silicon is dry, I do not recommend pinching or squeezing around the solder pad connection points. I just let mine hang loose, they are fine.
Now connect all the lights as if you were going to turn them on but DO NOT PLUG THEM IN TO THE WALL!! As you are connecting everything, double check that all your colored wires are matching up at the housings!!
Now, you should do one more continuity test before plugging them in since you did all this work. At the end of the last strip there are 6 holes for adding a Phillips Hue extension. I bent 6 male pins and inserted them in here in a way that they do not touch each other so I could gator clip each, one at a time, and test to again make sure there is not continuity between any 2 of the 6 lines.
As you'll notice, since all the light strips and cat 5 are connected together now, this final test at this end location with these 6 pins will test the entire line.
BE SURE TO PULL THOSE PINS OUT WHEN YOU ARE DONE TESTING BEFORE PLUGGING IN THE LIGHTS!!!
Once all 6 bent test pins are removed from the end of the light strip, go ahead and plug them in and test them! I tested mine before I finished hanging them.
Step 6: Final Result
It's a bit of time and work, but to me it was better than buying 3 strips @ $90 a pop with 3 separate plugs! Oh and cutting off all that waste and not being able to reuse it. I used all 6 ft by doing a 12", 24" and a 36" strip for the 3 sections of my cabinets and it fit great!