Balarama represents plowing the land for agriculture and therefore always carries in His hand a plow, whereas Krsna tends cows and therefore carries a flute in His hand. Thus the two brothers represent krsi-raksya and go-raksya

Expressions researched:
"Balarāma represents plowing the land for agriculture and therefore always carries in His hand a plow, whereas Kṛṣṇa tends cows and therefore carries a flute in His hand. Thus the two brothers represent kṛṣi-rakṣya and go-rakṣya"

Srimad-Bhagavatam

SB Canto 10.1 to 10.13

Vasudeva's father, Śūrasena, married a vaiśya girl, and from her Nanda Mahārāja was born. Later, Nanda Mahārāja himself married a vaiśya girl, Yaśodā. Therefore his family is celebrated as a vaiśya family, and Kṛṣṇa, identifying Himself as their son, took charge of vaiśya activities (kṛṣi-go-rakṣya-vāṇijyam (BG 18.44)). Balarāma represents plowing the land for agriculture and therefore always carries in His hand a plow, whereas Kṛṣṇa tends cows and therefore carries a flute in His hand. Thus the two brothers represent kṛṣi-rakṣya and go-rakṣya.

SB 10.5.20, Translation and Purport

When Vasudeva heard that Nanda Mahārāja, his very dear friend and brother, had come to Mathurā and already paid the taxes to Kaṁsa, he went to Nanda Mahārāja's residence.

Vasudeva and Nanda Mahārāja were so intimately connected that they lived like brothers. Furthermore, it is learned from the notes of Śrīpāda Madhvācārya that Vasudeva and Nanda Mahārāja were stepbrothers. Vasudeva's father, Śūrasena, married a vaiśya girl, and from her Nanda Mahārāja was born. Later, Nanda Mahārāja himself married a vaiśya girl, Yaśodā. Therefore his family is celebrated as a vaiśya family, and Kṛṣṇa, identifying Himself as their son, took charge of vaiśya activities (kṛṣi-go-rakṣya-vāṇijyam (BG 18.44)). Balarāma represents plowing the land for agriculture and therefore always carries in His hand a plow, whereas Kṛṣṇa tends cows and therefore carries a flute in His hand. Thus the two brothers represent kṛṣi-rakṣya and go-rakṣya.