Question

Factorize a2-b2-2b-1

Answer 1

a² - b² - 2b - 1

= a² - ( b + 2b + 1 )²

= a² - ( b + 1 ) ²

= a² -( b² + 1² + 2b1 )

= a² - b² + 1² +2b

Answer 2

Answer:

$Factors \: of \\a^{2}-b^{2}-2b-1\\=(a+b+1)(a-b-1)$

Step-by-step explanation:

$Factorisation \: of \\a^{2}-b^{2}-2b-1$

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

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

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

/*By algebraic identity:

x²+2xy+y² = (x+y)² */

$=[a+(b+1)][a-(b+1)]$

/* By algebraic identity:

x²-y² = (x+y)(x-y) */

$= (a+b+1)(a-b-1)$

Therefore,

$Factors \: of \\a^{2}-b^{2}-2b-1\\=(a+b+1)(a-b-1)$

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