Matthew 5:20-26 You have heard it said, but I say to you

Jesus said to his disciples:
"I tell you,
unless your righteousness surpasses that
of the scribes and Pharisees,
you will not enter into the Kingdom of heaven."

"You have heard that it was said to your ancestors,
You shall not kill; and whoever kills will be liable to judgment.
But I say to you, whoever is angry with his brother
will be liable to judgment,
and whoever says to his brother, Raqa,
will be answerable to the Sanhedrin,
and whoever says, 'You fool,' will be liable to fiery Gehenna.
Therefore, if you bring your gift to the altar,
and there recall that your brother
has anything against you,
leave your gift there at the altar,
go first and be reconciled with your brother,
and then come and offer your gift.
Settle with your opponent quickly while on the way to court.
Otherwise your opponent will hand you over to the judge,
and the judge will hand you over to the guard,
and you will be thrown into prison.
Amen, I say to you,
you will not be released until you have paid the last penny."

In this passage we see Jesus elaborating on the Commandments. He is explaining the limits of the law and reinterpreting them. The reason this section is found in the sermon on the mount is because Matthew is making the connection between Jesus and Moses. Just like Moses received the Law from God on the Mountain, so Jesus will expand on the laws and deliver them to the people from a mountain. The official title of this section is called Expounding the law.