Answer
$(2x-1+3y)(2x-1-3y)$
Work Step by Step
The first $3$ terms of the given expression, $
4x^2-4x+1-9y^2
,$ is a perfect square trinomial. Hence, the factored form is
\begin{array}{l}\require{cancel}
(2x-1)^2-9y^2
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the sum and difference of like terms, then the completely factored form of the expression, $
(2x-1)^2-9y^2
,$ is
\begin{array}{l}\require{cancel}
[(2x-1)+3y][(2x-1)-3y]
\\\\=
(2x-1+3y)(2x-1-3y)
.\end{array}
