algebra precalculus - How to determine if $2+x+y$ is a factor of $4-(x+y)^2$?

I know it is a factor but how could have I determined that it was? Feel free to link whatever concept is needed than solve it. Studying for clep and it's one of the practice problems. When I expand it I get nonsense.

Answer

Use difference of squares:

$$4 - (x+y)^2 = 2^2 - (x+y)^2 = (2 - (x+y))(2+(x+y)).$$