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