Answer
The number to add is $9$.
The factored form is $(y-3)^2$.
Work Step by Step
The given expression is $y^2-6y$.
This is in the form of $y^2-by$ where $b=6$.
To find the number needed to complete the square, use the formula $\left(\frac{1}{2}b\right)^2$.
$\Rightarrow \left(\frac{1}{2}b\right)^2=\left(\frac{1}{2}\cdot 6\right)^2=3^2=9$
Add $9$ to the given expression.
$=y^2-6y+9$
$=y^2-2\cdot 3 \cdot y+3^2$
Use the special formula $a^2-2ab+b^2=(a-b)^2$ where $a=y$ and $b=3$.
$=(y-3)^2$
Hence, the factored form is $(y-3)^2$.
