A computer slowing down after a while is not unusual, there are a few common causes and solutions
1) Malware. No matter how careful one is, there is some kind of malware able to get into a system. This guide explains steps (yes, more than one) that should be taken to remove any malware
http://www.tomshardware.com/forum/248626-45-simple-free-guide-removing-malware
2) Heat. On laptops especially, heat is a big concern. Ensuring that the laptop is used on a flat, hard surface and the vents are clear while on will go far to keep the laptop happy and running smoothly. A cooling pad helps here also.
3) Dust. Related to heat, dust gets into the heat sink of a laptop and effectively 'chokes' the cooling airflow. Blowing out the vents with compressed air may help - if dust bunnies have formed, disassembly and cleaning would be required since compressed air will not remove them.
You may be able to upgrade the ram but I would look at the above options first
This should be helpful