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

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To factor the perfect square trinomial $$ 4y^{2} - 20y + 25 $$, follow these steps:

1. **Identify the Structure:**
   
   A perfect square trinomial has the form:
   $$
   (ay + b)^2 = a^2y^2 + 2aby + b^2
   $$
   or
   $$
   (ay - b)^2 = a^2y^2 - 2aby + b^2
   $$

2. **Determine $$ a $$ and $$ b $$:**
   
   Compare $$ 4y^{2} - 20y + 25 $$ with the general form $$ (ay - b)^2 $$:
   
   - $$ a^2y^2 = 4y^2 $$ ⇒ $$ a^2 = 4 $$ ⇒ $$ a = 2 $$
   - $$ b^2 = 25 $$ ⇒ $$ b = 5 $$

3. **Verify the Middle Term:**
   
   Check if the middle term matches:
   $$
   -2ab y = -2 \times 2 \times 5 \times y = -20y
   $$
   This matches the given middle term $$ -20y $$.

4. **Write the Factored Form:**
   
   Using the values of $$ a $$ and $$ b $$, the factored form is:
   $$
   (2y - 5)^2
   $$

**Final Answer:**
$$
(2y - 5)^{2}
$$
$$ (2y - 5)^2 $$

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

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