dU=dq + dW(expansion) + dW(additional), give some examples of additional work...
Firstly, dq= du + dw. In thermodynamics, we assume all thermodynamic processes to be quasi-static (i.e. very very slow process). Assuming a process to be very very slow, you won't have any extra addition work done i.e. whatever heat you supply to the system is used up for increasing the internal energy of the gas and for work done by the gas against the external surrounding.
Now lets say if we didn't assumed thermodynamic process to be quasi-static. In this situation, if you apply heat to the system, it would increase the internal energy of the gas, and some part of the applied heat will be used up for the work done by gas against surrounding , and now as the process is not quasi-static, when the gas starts doing work by expansion of the piston, as the process is no longer slow, the piston will acquire some velocity and hence it would acquire a kinetic energy. And hence you will now have another work done. This additional work done is work done for the movement of piston. So if the process is not quasi-static, whenever you apply heat, that heat is used up in increasing the internal energy of the gas, used for work which is done by the gas against the surrounding and also an additional work which is work done to move the piston.
If you assumed the process to be quasi-static, then velocity of the piston during the expansion is approximated as zero and hence no kinetic energy of the piston and hence work done for the movement of piston is neglected. So whatever heat you applied will be utilised for increasing the internal energy of the gas and for the work done by the gas against the surrounding (and no extra additional work done)