Commentaries:
Jamieson, Fausset, and Brown
Genesis 21:10, Genesis 21:12, where Sarah's words are, "shall not be heir with my son, even with Isaac." But what was there said literally, is here by inspiration expressed in its allegorical spiritual import, applying to the New Testament believer, who is antitypically "the son of the free woman." In John 8:35-36, Jesus refers to this.
Cast out—from the house and inheritance: literally, Ishmael; spiritually, the carnal and legalists.
shall not be heir—The Greek is stronger, "must not be heir," or "inherit."
Other Jamieson, Fausset, and Brown entries containing Galatians 4:30:
Genesis 21:12
John 8:35
Galatians 4:31
1 Thessalonians 2:13
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