Factorize x² − 1 − 2a − a²
Question:
Factorize: \[ x^2 – 1 – 2a – a^2 \]
Solution
Rearranging the terms:
\[ x^2 – 1 – 2a – a^2 = x^2-(a^2+2a+1) \]
\[ = x^2-(a+1)^2 \]
Using the identity
\[ A^2-B^2=(A-B)(A+B) \]
Therefore,
\[ x^2-(a+1)^2 = (x-(a+1))(x+(a+1)) \]
\[ = (x-a-1)(x+a+1) \]
Therefore,
\[ \boxed{(x-a-1)(x+a+1)} \]