إإنضم is if I remember the 7'th form (InFa3ala) of the verb DDAMMA, which usualy is the passive form of the root-verb, so to be included hence become member .... If you know the meaning of the root verb, you can offen guess the meaning of it's derived forms like: ROOT: 3aLaMa to know FORM 23aLLama to let know --to teach ta3allama

ضم= included انضم= join شمل= included (more comprehensive) ضم like you speak about something that include many details انضم it mean join for something like انظم احمد الى الفريق شمل it is good if you want to explain something that include many other things , for instance, المناقشة شملت عده نواحي فكرية و اقتصادية

ضم ان يقوم ما بضم شي الى اخر او مجموعة, ضمت الام ولدها انضم ان يقوم هو بالانضام من تلقاء نفسه كان نقول انضم اللاعب الى الفريق شمل بالاغلب نقول شمل عندما نريد تفصيل ما اشتمل عليه الموضوع كان نقول اشتملت الرواية على جوانب متعددة