Expanding the given expression:

4x(a+x+y) + 4a(a-x-y) - 4y(x-a-y)
= 4ax + 4x^2 + 4xy + 4a^2 - 4ax - 4ay - 4yx + 4ay - 4y^2
= 4ax + 4x^2 + 4xy + 4a^2 - 4ax - 4ay - 4xy + 4ay - 4y^2
= 4x^2 + 4a^2 - 4y^2

Therefore, 4x(a+x+y) + 4a(a-x-y) - 4y(x-a-y) simplifies to 4x^2 + 4a^2 - 4y^2.