Answer
$4(x-1)^2$
Work Step by Step
Factoring the $GCF=4,$ the given expression, $
4x^2-8x+4
,$ is equivalent to
\begin{align*}\require{cancel}
&
4(x^2-2x+1)
.\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the trinomial expression above has $c=
1
$ and $b=
-2
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-1,-1
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{align*}
&
4(x-1)(x-1)
\\&=
4(x-1)^2
.\end{align*}
Hence, the factored form of the given expression is $
4(x-1)^2
$.
