SB 9.10.2

tasyāpi bhagavān eṣa
 sākṣād brahmamayo hariḥ
aṁśāṁśena caturdhāgāt
 putratvaṁ prārthitaḥ suraiḥ
rāma-lakṣmaṇa-bharata-
 śatrughnā iti saṁjñayā
Word for word: 
tasya — of him, Mahārāja Daśaratha; api — also; bhagavān — the Supreme Personality of Godhead; eṣaḥ — all of them; sākṣāt — directly; brahma-mayaḥ — the Supreme Parabrahman, the Absolute Truth; hariḥ — the Supreme Personality of Godhead; aṁśa-aṁśena — by an expansion of a plenary portion; caturdhā — by fourfold expansions; agāt — accepted; putratvam — sonhood; prārthitaḥ — being prayed for; suraiḥ — by the demigods; rāma — Lord Rāmacandra; lakṣmaṇa — Lord Lakṣmaṇa; bharata — Lord Bharata; śatrughnāḥ — and Lord Śatrughna; iti — thus; saṁjñayā — by different names.
Translation: 
Being prayed for by the demigods, the Supreme Personality of Godhead, the Absolute Truth Himself, directly appeared with His expansion and expansions of the expansion. Their holy names were Rāma, Lakṣmaṇa, Bharata and Śatrughna. These celebrated incarnations thus appeared in four forms as the sons of Mahārāja Daśaratha.
Purport: 

Lord Rāmacandra and His brothers, Lakṣmaṇa, Bharata and Śatrughna, are all viṣṇu-tattva, not jīva-tattva. The Supreme Personality of Godhead expands into many, many forms. Advaitam acyutam anādim ananta-rūpam. Although they are one and the same, viṣṇu-tattva has many forms and incarnations. As confirmed in the Brahma-saṁhitā (5.39), rāmādi-mūrtiṣu kalā-niyamena tiṣṭhan. The Lord is situated in many forms, such as Rāma, Lakṣmaṇa, Bharata and Śatrughna, and these forms may exist in any part of His creation. All these forms exist permanently, eternally, as individual Personalities of Godhead, and they resemble many candles, all equally powerful. Lord Rāmacandra, Lakṣmaṇa, Bharata and Śatrughna, who, being viṣṇu-tattva, are all equally powerful, became the sons of Mahārāja Daśaratha in response to prayers by the demigods.