The story of Moses and the brazen serpent appears multiple times in the Book of Mormon and is also alluded to throughout the text.
Neal Rappleye notes how the story is told in different ways for different purposes. For example, Nephi’s first telling of the story emphasizes those whose did not look on the serpent (in reaction to Laman and Lemuel’s rebelliousness), whereas Nephi’s second telling of the story emphasizes how the serpent symbolized Jesus Christ (when teaching “proving unto my people the truth of the coming of Christ”).
The brazen serpent is also mentioned in the Book of Mormon alongside Near Eastern serpent symbolism such as:
As illustrated by the various references made throughout this paper, when later Nephite writers mentioned the brazen serpent narrative, in each instance, they generally interpret it along the same lines Nephi did, specifically using same name-titles (Messiah, Son of God) and talking about qualities and attributes of Christ (atonement, eternal life, rising from the dead, resurrection, judgment) that relate to ancient Near Eastern serpent symbolism. In many cases, these are features that are specifically associated with the seraph-serpent in pre-exilic Israelite texts (i.e., Numbers 21:4–9; Isaiah 6; 14:28) and iconography. Thus, with his two retellings of the brazen serpent narrative, Nephi evidently established a standard interpretation of the story that other Nephite writers adopted with minimal change.
It should be noted, however, that there are some key developments in how the story is used and interpreted within the text. They are modest, even subtle, developments that make sense as natural outgrowths of how Nephi used the story. Similar innovations of interpretation show up in the ancient Judeo-Christian tradition, and do so in response to similar circumstances and pressures. Thus, the Book of Mormon authentically reflects a living interpretative tradition.– Neal Rappleye – Serpents of Fire and Brass: A Contextual Study of the Brazen Serpent Tradition in the Book of Mormon
How would Joseph Smith have understood the brazen serpent story so well and be aware of so much Near Eastern symbolism like this?