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Which of the following is the factors of $x 2 − y 2 − 2 y − 1$ ?

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(x - y - 1) (x + y + 1)

(x + y - 1) (x + y + 1)

(x - y - 1) (x - y + 1)

(x - y + 1) (x + y + 1)

answer is A.

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Detailed Solution

Given,

x 2 − y 2 − 2 y − 1

We know that,

a 2 − b 2 = a + b a − b

⇒ x 2 − y 2 − 2 y − 1 ⇒ x 2 − y 2 + 2 y + 1 ⇒ x 2 − y 2 + 2 × y × 1 + 12 ⇒ x 2 − y + 1 2

⇒ x − y + 1 x + y + 1 ⇒ x − y − 1 x + y + 1

Hence, factors of

x 2 − y 2 − 2 y − 1 = x − y − 1 x + y + 1

.
Therefore, option 1 is correct.

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