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

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:** \[ (2y - 5)^{2} \]