Question

1. factor: 4y² - 20y + 25

Explanation:

Step1: Identify the form

This is a quadratic trinomial of the form $ax^{2}+bx + c$ (here $x = y$, $a = 4$, $b=-20$, $c = 25$). Notice it may be a perfect - square trinomial. The formula for a perfect - square trinomial is $(m - n)^2=m^{2}-2mn + n^{2}$.

Step2: Check if it's a perfect - square trinomial

For $4y^{2}-20y + 25$, we have $4y^{2}=(2y)^{2}$ and $25 = 5^{2}$, and $2\times(2y)\times5=20y$. So, $4y^{2}-20y + 25=(2y - 5)^{2}$.

Answer:

$(2y - 5)^{2}$