CLAIM: Is Paul’s citation of Isaiah 54 out of context, or does this help him build upon his argument?
RESPONSE: The context for Isaiah 54 is the Babylonian Exile. The people were sent into Exile, because they couldn’t keep the Law. Therefore, the law resulted in the Exile for the people. However, Isaiah writes that they could “rejoice” and “break forth and shout” because of God’s promise to rescue them—not because of their works (see Isa. 54:8-10). Therefore, Paul shows that the Law brings exile and death, but the promise brings “rejoicing.” This helps Paul to build his case for following Christ through faith and not through law.
There is an additional element in this passage which shows that the Jewish people were not the locus of God’s bearing of fruit. Cole writes, “Even for an ‘orthodox’ Jewish Christian of the time of Paul, it must have come as a shock to realize that Gentile Christians already far outnumbered Jewish Christians, a fact which we accept without thinking today. Stranger still, the time would come when the Gentile Christian church would far outnumber unbelieving Jewry. Then indeed the words of this prophecy would find fulfilment: the desolate will have more children than her that is married (literally, ‘has a husband’).” This would fit with the “allegory” mentioned above about Sarah bearing children—even though she was barren. In essence, the Gentiles are bearing fruit—even though they too were formerly “barren.”
 Cole, R. A. (1989). Galatians: an introduction and commentary (Vol. 9, p. 184). Downers Grove, IL: InterVarsity Press.