Factor the perfect square trinomial: \( 4y^{2} - 20y + 25 \)

To factor the perfect square trinomial \( 4y^{2} - 20y + 25 \), we start by recognizing that it can be expressed in the form \( (ay - b)^{2} \). The first term, \( 4y^{2} \), can be rewritten as \( (2y)^{2} \), and the last term, \( 25 \), is \( 5^{2} \). Now, we check twice the product of the outer factors, which is \( 2 \cdot 2y \cdot 5 = 20y \). So, we can factor the trinomial as: \[ (2y - 5)^{2} \] Now let's summarize: The factored form of \( 4y^{2} - 20y + 25 \) is \( (2y - 5)^{2} \).