Answer
$2(2x-1)(2x-1)$ or
$2(2x-1)^{2}$
Work Step by Step
$8x^{2}-8x+2$
Factor out greatest common factor $2$
$=2(4x^{2}-4x+1)$
In this trinomial $(4x^{2}-4x+1)$, $a=4$, $b=-4$ and $c=1$.
Splitting the middle term $b$ into two numbers whose product is $4$ $(a \times c)$ and whose sum is $(b)$ $-4$. The numbers are $-2$ and $-2$.
$=2(4x^{2}-2x-2x+1)$
Factor out by grouping.
$=2((4x^{2}-2x)+(-2x+1))$
$=2(2x(2x-1)-1(2x-1))$
$=2((2x-1)(2x-1))$
$=2(2x-1)(2x-1)$
$=2(2x-1)^{2}$
