Some Bibles title this paragraph, “Jesus Fulfills the Law.”The sense in which many professing Christians use the term “fulfills” is not inspired Scripture. In this case, it does not mean “accomplishes by keeping” or “does away with,” as judged against what He taught in what immediately follows. Fulfills, in this case, means “fills to the full,” “fully exemplifies the conduct it covers,” or “expands to its fullest intent.” Consider His subsequent illustrations carefully:

You have heard that it was said to those of old, “You shall not murder, and whoever murders will be in danger of the judgment.” But I say to you that whoever is angry with his brother without a cause shall be in danger of the judgment. And whoever says to his brother, “Raca!” shall be in danger of the council. But whoever says, “You fool!” shall be in danger of hell fire. Therefore if you bring your gift to the altar, and there remember that your brother has something against you, leave your gift there before the altar, and go your way. First be reconciled to your brother, and then come and offer your gift. Agree with your adversary quickly, while you are on the way with him, lest your adversary deliver you to the judge, the judge hand you over to the officer, and you be thrown into prison. Assuredly, I say to you, you will by no means get out of there till you have paid the last penny. (Matthew 5:21-26)

His teaching shows Him raising the acceptable level of obedience far higher than what people ordinarily considered as satisfactory behavior. Jesus expands the scope of sin in the sixth commandment from outright murder to also include a high level of anger in certain situations! Matthew 5:27-30 shows the same pattern in this teaching on the seventh commandment:

You have heard that it was said to those of old, “You shall not commit adultery.” But I say to you that whoever looks at a woman to lust for her has already committed adultery with her in his heart. If your right eye causes you to sin, pluck it out and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell. And if your right hand causes you to sin, cut it off and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell.

The same conclusion is true of this commandment and also for each of the others He expands during His Sermon on the Mount. Far from doing away with God's commandments, He raises the standards of acceptable behavior far higher.