From ‘Sahih al-Adab al-Mufrad’ (757):
Abu Hurayrah reported that a man passed by the Messenger of Allah while he was in a gathering, and he said: “as-Salamu ‘alaykum.” So, he said: “Ten good deeds.”
Another man passed by and said: “as-Salamu ‘alaykum wa Rahmatullah.” So, he said: “Twenty good deeds.”
Another man passed by and said: “as-Salamu ‘alaykum wa Rahmatullah wa Barakatuh.” So, he said: “Thirty good deeds.”
So, let us try to obtain the thirty good deeds by making the complete greeting instead of the basic one. Imagine how many hasanat pass us by every time we greet each other, as just two or three extra words will gain us an extra twenty good deeds each time we say them!
And from ‘as-Silsilah as-Sahihah’ (1403): “If a man meets his Muslim brother, he should say: ‘as-Salamu ‘alaykum wa Rahmatullah wa Barakatuh.'”