4) This expression can be factored as (x^2 - 2xy + y^2) - (2x^2 - 4xy + 2y^2). The first part is a perfect square trinomial, which can be factored as (x - y)^2. The second part can be factored as 2(x^2 - 2xy + y^2), which is 2(x - y)^2. Therefore, the expression can be written as (x - y)^2 - 2(x - y)^2, or (1 - 2)(x - y)^2, which simplifies to -1(x - y)^2.

5) This expression can be factored by grouping. First, factor out the greatest common factor, which is x^2, to get x^2(x - 4) - 8(x - 4). Now, factor out the common factor of (x - 4) to get (x - 4)(x^2 - 8). The expression is now fully factored as (x - 4)(x^2 - 8).

6) This expression can be factored as (x + y)^2 - 2(x + y) + 1. The first part is a perfect square trinomial, which can be factored as (x + y - 1)^2. Therefore, the expression can be written as (x + y - 1)^2.