Which Of the following is a factor of 4-(x+y)^2?

In your original equation substitute z=(x+y) and then you have 4-z^2 which can be factored out to (2-z)(2+z)

Substitute z back in [2-(x+y)][2+(x+y)] which is (2-x-y)(2+x+y)

a^2 – b^2 = (a-b) (a+b)

4 – (x+y)^2 =

2^2 – (x+y)^2 = (2 – x – y) (2+x +y)

where a = 2

b = (x+y)

so, C: is the answer