What a good question.
What was the context in which the term "Works of the Law" was first used?
Rom, 3:
23 For all have sinned, and come short of the glory of God;
All have Transgressed God's Commandments. The wages of the transgression is death. "the soul that sin's shall die".
So because we have sinned, we can't "live" forever, we "Die" forever. So something needs to be done to justify, remove or cleanse this sin from us in order for us to "Live".
So in Moses time there was a law created to deal with this issue of removing sin. "It was, as Paul says in Gal. 3:19, "ADDED because of transgression (sin) until the Seed should come. This Added Law was called the "Levitical Priesthood". (Heb. 7-10)
Heb. 9:
1 Then verily the first
covenant had also
ordinances of divine service, and a worldly sanctuary.
This "Priesthood" was a shadow of what the Messiah would do to remove, cleanse, and justify the sins of the people.
When we sinned, we would seek out a "Levite" priest that God had separated specifically for this purpose.
Num. 8:
11 And Aaron shall offer the Levites before the LORD
for an offering of the children of Israel,
that they may execute the service of the LORD.
This service was two fold, #1. They gave God's Laws to His people. #2. They performed sacrificial, ceremonial "Works of the Law" for the removal, justification and cleansing of sin.
This is the "Covenant" God made with the Children of Israel that was "Added" because of the transgress of the covenant or promise gave to Abraham. (See Gen. 26: 4&5)
Ex. 2:
23 And it came to pass in process of time, that the king of Egypt died: and the children of Israel sighed by reason of the bondage, and they cried, and their cry came up unto God by reason of the bondage.
24 And God heard their groaning,
and God remembered his covenant with Abraham, with Isaac, and with Jacob.
25 And God looked upon the children of Israel, and God had respect unto
them.
But this "Priesthood" for administration of the God's Commandments and for remission of sins was not to last forever.
Jer. 31:
31 Behold, the days come, saith the LORD,
that I will make a new covenant with the house of Israel, and with the house of Judah:
32 Not according to the covenant that I made with their fathers in the day
that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD:
33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
No more will we need to find a "Levite Priest" to show us God's Laws, or cleanse us from our sins. God will intervene directly.
But the Mainstream God of Abraham preaching people of Jesus time didn't believe He was the Messiah. Even after He showed them in the scriptures, healed people and forgave people without ever using a single drop of goats blood as prescribed by the "works of the Law". Even after He was raised from the dead, they still rejected His blood and His Sacrifice for the removal, justification or cleansing of sins. They rejected God's prophesied "New Covenant" and continued in the Old Covenant of preaching and performing Levitical Priesthood sacrificial, ceremonial "works and Deeds of the Law" for removal of sins. And they persecuted, even killed anyone who taught differently. Jesus fought with them and Paul and Peter fought with them through out their whole lives according to scripture.
That's brings us to Rom. 3:
1 What advantage then hath the Jew? or what profit
is there of circumcision?
2 Much every way: chiefly, because that unto them were committed the oracles of God.
3 For what if some did not believe?
shall their unbelief make the faith of God without effect?
God forbid!
Just because the Mainstream congregation of that time didn't believe in God's Words, doesn't make God's Word void.
Jesus is the Messiah, and He did usher in the "New Covenant" as prophesied by the Prophets of old.
Rom. 3:
20 Therefore by the
deeds of the law there shall no flesh be justified in his sight: for by the law
is the knowledge of sin.
21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
"
for I will forgive their iniquity, and I will remember their sin no more." "the Just shall "LIVE" by Faith"
22 Even the righteousness of God
which is by faith of/in Jesus Christ unto all and upon all them that believe: for there is no difference:
So this is the context of the term "works of the Law" (faith in Levitical Priesthood duties)" vs. faith in the blood of Christ.
This has absolutely nothing in common with "works worthy of repentance that is required of us. Or the work of "Submitting ourselves unto the Righteousness of God" of the work of "Studying to show ourselves approved of God", or most importantly, living in obedience to God by following His Commandments rather than doctrines and traditions of men.
There are pages of scripture that prove this true according to the Bible, but to keep this post shorter, I have only chosen a few. I would be glad to show the rest to anyone who is interested.
Great topic, great question