\(8x^2-12xy+4y^2-2x-1\)
\(=9x^2-2.3x.2y+4y^2-x^2-2x-1\)
\(=\left(3x-2y\right)^2-\left(x^2+2x+1\right)\)
\(=\left(3x-2y\right)^2-\left(x^2+2x+1\right)\)
\(=\left(3x-2y\right)^2-\left(x+1\right)^2\)
\(=\left(3x-2y+x+1\right)\left(3x-2y-x-1\right)\)
\(=\left(4x-2y+1\right)\left(2x-2y-1\right)\)