Question:
Factorise:
x2 − y2 − 2y − 1
Solution:
We have:
$x^{2}-y^{2}-2 y-1=x^{2}-\left(y^{2}+2 y+1\right)$
$=(x)^{2}-(y+1)^{2}$
$=\{x+(y+1)\}\{x-(y+1)\}$
$=(x+y+1)(x-y-1)$
$\therefore x^{2}-y^{2}-2 y-1=(x+y+1)(x-y-1)$
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