The expression \(4x^2 - 4xy + y^2\) can be factored. To do this, we look for a way to rewrite it as a product of binomials.

Notice that the expression resembles a perfect square trinomial. A perfect square trinomial takes the form \(a^2 - 2ab + b^2\) or \(a^2 + 2ab + b^2\), which factors to \((a - b)^2\) or \((a + b)^2\), respectively.

In this case, we can rewrite \(4x^2 - 4xy + y^2\) as follows:

\[4x^2 - 4xy + y^2 = (2x)^2 - 2(2x)(y) + y^2\]

This matches the form \(a^2 - 2ab + b^2\) where \(a = 2x\) and \(b = y\). Therefore, it can be factored as:

\[(2x - y)^2\]

So, the factored form of \(4x^2 - 4xy + y^2\) is:

\[(2x - y)^2\]