Answer
$(2y-3)^2$
Work Step by Step
Let $z=(2y-1).$ Then the given expression, $
(2y-1)^2-4(2y-1)+4
,$ is equivalent to
\begin{array}{l}\require{cancel}
z^2-4z+4
.\end{array}
The two numbers whose product is $ac=
1(4)=4
$ and whose sum is $b=
-4
$ are $\{
-2,-2
\}$. Using these two numbers to decompose the middle term of the expression, $
z^2-4z+4
,$ then
\begin{array}{l}\require{cancel}
z^2-2z-2z+4
\\\\=
(z^2-2z)-(2z-4)
\\\\=
z(z-2)-2(z-2)
\\\\=
(z-2)(z-2)
\\\\=
(z-2)^2
.\end{array}
Since $z=(2y-1)$, then the expression $
(z-2)^2
$ is equivalent to
\begin{array}{l}\require{cancel}
(2y-1-2)^2
\\\\=
(2y-3)^2
.\end{array}
