Determine the value we need to add to the equation to make it a perfect square trinomial, then factor it.
$y^{2} - 10 y +$ __

$5;$\left$(y-5$\right$)^2$

$25;$\left$(y+5$\right$)^2$

$25;$\left$(y-5$\right$)^2$

$5;$\left$(y+5$\right$)^2$

Verified step by step guidance

Identify the given expression: $y^2 - 10y + \_$, where we need to find the missing constant term to complete the perfect square trinomial.

Recall that a perfect square trinomial has the form $(y - a)^2 = y^2 - 2ay + a^2$. Here, the coefficient of $y$ is $-10$, which corresponds to $-2a$.

Solve for $a$ by setting $-2a = -10$, which gives $a = 5$.

Calculate the constant term to add by squaring $a$: $a^2 = 5^2 = 25$. This is the value to add to complete the perfect square trinomial.

Write the completed trinomial and factor it as $(y - 5)^2$.

Master Complete the Square with a bite sized video explanation from Patrick Ford

Determine the value we need to add to the equation to make it a perfect square trinomial, then factor it.y2−10y+y^2-10y+ __