There was historical rivalry between Arab and Persian in Period of Persian Empire , Sassanian Empire Continued their Humiliate against puppet state of Akhmeids (Nua’aman), Akhmeids started to hate Persian and they need to kick Persian out , so they were in war with Arabic Byzantine puppet state so they went to their Arabian Blood-brothers . that is the first reason.
the second reason was Persia was Zoroastrian religion , and Arab was Muslims so they need to spread Islam in Persia to success the Prophet Mohammed Prophecy that “Muslims will rule Persia and Rome” .
third reason Persia was very weak so you could invade it faster than Roman and get new manpower for next invades .
Many of Persians converted to Islam before invade , so they support Islamic invade.
that is my opinion with some of historical facts to invade Persia.