Wire that short can t be spliced or extended.
How to extend electrical wire inside wall.
You will need to reroute these cables to a different junction box somewhere the wiring is able reach with the needed spare length inside the box.
With the exception of switch boxes that do not have a neutral wire and switch controlled fixtures at the end of a circuit to extend a circuit you can simply tap into that circuit at any easily accessible receptacle switch fixture or junction box.
Next run wire from the existing junction box to each box base.
The method is called a western union splice where you join two ends.
Drill one hole through every stud.
Splices need to be done inside a junction box and those junction box must remain accessible once the wall is closed up.
Published on dec 30 2015 a quick demonstration on how to join up the electrical wire when cutting it and adding an extension.
The wire must be able to come out beyond the surface of the box at least 3.
Avoid nicking or scratching the copper wire while removing the insulation.
If you don t want to re run longer cables you ll need to splice in some additional cable.
When working with electrical you will run into a situation where someone didn t leave enough slack inside the electrical box.
Use the labeled notches on a wire stripper to check the gauge of the existing wire 14 gauge is most common but you may have 12 gauge wire.
Drill left to right or right to left through a wall stud with power drill and a 1 1 4 inch bit working through the access openings that you cut in the drywall.
You ve pretty well identified your two choices.
Insert a clamp with wires attached into the junction box hole and from inside the box push the included nut over the wires and onto the clamp threads.
The size of the wire you add must match the size of the existing wire.