Question

Factorize:

$a^2-b^2-2b-1$

• A. $[a-b-1][a-b-1]$
• B. $[a-b-1][a+b+1]$
• C. $[a+b+1][a-b+1]$
• D. $[a-b+1][a+b-1]$

Answer 1

The correct option is B

$[a-b-1][a+b+1]$

$\Rightarrow a^2-b^2-2b-1$

$\Rightarrow a^2-(b^2+2b+1)$

$\Rightarrow a^2-(b+1{)}^2$

$\because (a+b{)}^2=a^2+b^2+2ab,and{a}^2-b^2=(a-b\left)\right(a+b)$

$\Rightarrow [a-(b+1\left)\right][a+(b+1\left)\right]$

$\Rightarrow [a-b-1][a+b+1]$