how to get rid of the copyrighted material flag from YouTube, Facebook & other videos

Hello, I'm new to this and using this forum to educate myself on DRM protection. When I put a little video together of the kids playing with a little music clip added, what is it that flags, on say facebook or Youtube that there is copy right protected material in the video, what actually is being detected? and how can I use the music I purchased in my videos of the kids without setting off flags? Thanks in advance for any help on the matter...