Complex sentence: The first caliphs, known as "al-khulafā' ar-rāshidūn" ("Rightly Guided Caliphs"), conquered significant parts of the Persian and Byzantine territories.
Split into simpler sentences: The first caliphs are known as "al-khulafā' ar-rāshidūn" ("Rightly Guided Caliphs"). Under them, the territory under Muslim rule expanded deeply into the parts of the Persian and Byzantine territories.