$$4x^{2}-y^{2}-2y-1$$
$\left(2x-y-1\right)\left(2x+y+1\right)$
$$4x^{2}-\left(y^{2}+2y+1\right)$$
$$\left(2x\right)^{2}-\left(1+y\right)^{2}$$
$$\left(2x-1-y\right)\left(2x+1+y\right)$$
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$-\left(y+1\right)^{2}+4x^{2}$