Simple but effective military tactics helped spread Islam because they were easy and not too complicated for the Muslims to carry out but hard for the enemy to defend. The Muslims tactics were to charge the enemy and cast a shower of javelins. They would repeat this until the enemy showed signs of breaking and then started hand to hand combat. They were usually outnumbered and the superiority of their enemies should have been overwhelming however, it wasn't and the Muslims rarely lost.
Other religions (Jews, Christians and Pagons) being attracted to Islam would help the Islamic faith to expand more quickly because people were more willing to accept it. They were willing to accept the new faith because they hated their rulers and wanted a change from high taxes and religious persecution.
The neighboring Byzantine and Persian empires were weak is a main point because the Muslims could defeat them more easily, as they had been fighting each other for a long time and by the time they faced the Muslims both empires were exhausted by war.
‘Berbers’ who were a North African tribe became Muslims helped to strengthen the Muslim’s army and as the tribe was a fierce fighting tribe it would scare and frighten opponents away, thus making it easier for Islam to spread.
In my opinion the most important factor of Islam’s expansion was that other religions were attracted to follow Islam. Many people whose countries had been taken over by Byzantine and Persian empires hated their rulers and welcomed the Muslim invaders for freeing them. Islam gave them knowledge and education; as Islam was the newest