Question

Factorize : x² − 1 − 2a − a²

Answer 1

The given expression to be factorized is

 `x^2 -1 -2a -a^2`

Take common -1from the last three terms and then we have 

`x^2 - 1 -2a - a^2`

` = x^2 - (1+2a + a^2)`

` = x^2 - {(1)^2 + 2.1.a+ (a)^2}`

` = x^2 - (1+ a)^2`

` = (x)^2 - (1+a)^2`

` = {x+ (1+ a)}{x-(1+a)}`

` = (x+1+a)(x-1-a)`

We cannot further factorize the expression. 

So, the required factorization is   `x^2 -1 -2a - a^2 = (x+1 + a)(x-1-a)`.