Start with the un-simplified side, (x+y)2
The expression (x+y)2 can be re-written as (x+y)(x+y).
The expression (x+y)(x+y) can be multiplied using the Distributive Property. That results in x2+xy+xy+y2.
The expression x2+xy+xy+y2 can be simplified by adding the middle terms. This results in x2+2xy+y2.
This proves that (x+y)2 = x2+2xy+y2.
I hope this helps clear things up!
