Why did muhammad return to mecca to conquer it after ten years?

Hey You!

As a Muslim, I know quite a lot about this!

I'm not sure how much you've been asked to write, so I'll provide a couple facts.

Prophet Muhammad returned to Mecca to defeat the Quraysh. They'd signed a treaty between the two muslim tribes, and kept peace for some time, but then the agression ignited once again in the Quraysh. The Prophet traveled during the beautiful month of Ramadan. They defeated the Quraysh, and settled it with them, and opened the entrance to Mecca. The Prophet died two years after this.

If you're talking about the Prophet Muhammad (s.a.w.) that Muslims consider their final Prophet, then as far as my knowledge stretches, we believe that he returned to Mecca because God revealed to him that it was time to go and take back his homeland; the very same homeland he had been kicked out of. 

There had been a treaty between him and his people, and the people who lived in Makkah, the place where he had been kicked out of. They were called the Quraysh. They had been warring for many years, ever since the Prophet first started to preach his religion, Islam, and his belief in one and only God. They signed a truce, called the TREATY OF HUDAIBIYAH, in which they decided they decided on peace.

(If the terms of the truce are needed, they are the following : (a) Whoever escapes Makkah and comes to Madinah without their captor/owner's permission, they will immediately be returned. (b) If anyone from Madinah goes to Makkah, then they have a right to keep them. (c) The Prophet will return in the following year to perform Umrah/Hajj, and will stay for three days' time. (d) If any (tribe) one wishes to make an alliance with the Prophet, so be it. If any (tribe) wishes to make an alliance with the people of Quraysh, so be it. These conditions are not in order. The treaty issued a 10-year peace.)

So basically, the Clan of Bani Bakr (I believe that's the name) allied with the Quraysh. After a few years of Peace, they ended up killing many men from anther tribe that had allied with the Prophet when they were drinking water from a well. (Bani Khuza'a, I believe. In that time, there were tribes and clans and everything.)

The leader of Quraysh, the leading clan in Makkah, went to the Prophet to appeal to him and make him re-consider what had happened, but no one would hear it. Many lives had been taken, and back then, it was considered unacceptable. The Prophet waited for a revelation, something from God, instructing him what to do.

And so began the conquest of Makkah. They headed towards Makkah to begin. It's believed that the Prophet did not tell anyone about where they were heading -- he had tell all prepare to travel, and they were sure not to take many weapons, for they wished to claim Makkah peacefully.)

That's basically the gist of it, with many details that you probably didn't need.