Factorise:

We have:

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

$=(x)^{2}-(y+1)^{2}$

$=\{x+(y+1)\}\{x-(y+1)\}$

$=(x+y+1)(x-y-1)$

$\therefore x^{2}-y^{2}-2 y-1=(x+y+1)(x-y-1)$