I went through a period like this way back when and it was because I wasn't challenged enough...I was bored with it. So, one thing you might look into is if he really can do it is to see if it is too easy and he just skims through the problems to say he's done so he can do something else. If that is the case, try to get him into a more advanced class or talk to his teacher to see if he/she can make it more interesting. Try to connect the school subject with something else he's interested in. For example, to create computer games, one needs to know math, coordinates, and equations as well as life lessons of cause and effect.
Unfortunately, I'm seeing this same behavior in my 7yo son and what has worked for him (so far) is 15 minutes of homework (without distractions -- away from the tv) and then 15 minutes of play or TV time. After that, I sit with him and go over what he did, and help him figure out what he got wrong and why. I do not tell him the answers but ask him questions to help him figure it out.
You may have to take time to work with him and actually sit with him while he does his homework and have him tell you how he arrives at the answers. If he says he did it in study hall, have him bring it home so you can see it and go over it with him. If he says "you don't trust me" tell him that he's betrayed your trust and needs to earn it again. The records show that he hasn't done what he said he would do and how would he feel if you didn't follow through on things he wanted/expected/needed from you??? Turn it around for him to think through and realize that he's doing more damage to the people around him and himself for now AND the future than he might realize. Most kids don't see the full effect of their actions or consider any effects of their actions beyond one or two steps away. But we've all seen how one bad apple at the top can spoil the entire bag...even the one farthest away. He needs to understand that it isn't just that his homework isn't being done correctly and getting bad grades, it's also that he is changing his relationships with you, the rest of the family, his school/teachers, as well as jeopardizing his future career which would limit the number and kinds of toys (video games, stereos, car, home, etc) and free time he can afford on his own.
My son likes to just guess and write something to have it done... I've told him that homework is like anything else...it will reflect the effort/concentration put into it. (Again, like a video game, if you don't pay attention, you lose...if you don't pay attention to homework, you lose. In both, if you lose, you have to repeat that same level and can't move forward in the game, school, or life, until it is completed.)
Good luck! and I'm sorry for the book! :)