Verses 19 and 20 of Matthew are absent. In their place are two new verses. The essential difference is that the Matthean verses were more specific to the congregation in the Old World, whereas these verses are more specific to the people in Bountiful and those to whom they would preach.
For the New World, Christ declares that he has come to give “the law the commandments of my Father.” That distinction between Jesus (Jehovah, whom the Nephites understood to be their God) and the Father, is one of the lessons being taught at this time.
Rather than the law that emphasized actions, Christ emphasizes a broken heart and a contrite spirit. It is not that those concepts were never previously required, but rather that they were being elevated in importance while the more communal aspects of religion, that were part of the law of Moses, were fulfilled.
The declaration is not that the people should become righteous, but rather that the individual person should become righteous. Each individual must keep Christ’s commandments, or not be able to enter into the kingdom of heaven.