What are signs of adhd?...I have a 4 yr old who seems to be alot more different than my 2 year old. (very long?

My 4yr old seems to always be the only one getting in trouble. He never listen and if he does it like once in a blue moon, he always hitting on his brothers and very impatient. for example...he asked me the other day to write down daddy on a piece of paper so he can copy it...so it did. he started to write it and then all of a sudden he kept messing up and wasnt gettin it right so he got mad so I told him to be patient and try again..he didn't what he ended up doing was getting really mad and starts to scribble all over the paper and stabbing the pen into the paper to where he actually broke the pen. after that he would throw himself down on the floor and start screaming, kicking, yelling and hitting whatever is around including his brothers.....another thing he doesnt like doing is listening. when I ask him to pick up all his toys he would say I didn't do that I don't wanna pick it up and then starts crying like if I had beat him to death or something.....also another thing is if he sees something he wants or likes on tv or whatever he would ask me if i can buy that for him and I would say yes....right after I say yes he would turn around and tell me " but mommy you keep saying no" when Im literaly telling him yes over and over........My son does get disciplined and he does get his lil wooped when he gets out of control but It doesnt help he just gets worst. He started school a 2 months ago and they said he's quite and doesnt really talk much and he is now starting to talk more in school and interact with the kids and activities that they do in school. He's a whole knew different person in school but when he comes home hes like the devil.....I just so fed up and I really dont know what to do at this point. Dont get me wrong hes a very smart and bright kids at age 4 he can write his first name and say the abc's...etc but I cant figure out his behavior towards me he is just constantly crying for every lil thing.