Question

please give answer with full explanation ( Factorise) x²-y²-2y-1​

Answer 1

QUESTION: Factorise : x² - y² - 2y - 1

SOLUTION:

Let take minus common in (-y² -2y -1), we get:

=> - ( y² + 2y + 1)

As we can see ( y² + 2y + 1 ) is making the identity of (a + b)² = a² + 2ab + b²

where, a = y

b = 1

So, y² + 2y + 1 = (y + 1)²

Hence, The factorization of (x² - y² - 2y - 1) is [ x² - (y + 1)² ]

So the required answer is => x² - (y² + 1)²

Answer 2

Answer:

${x}^{2} - {y}^{2} - 2y - 1$

let us take '-' common in

$( - {y}^{2} - 2y - 1)$

now we get

$- ( {y}^{2} + 2y + 1)$

where,a=y

b=1

so,

${y}^{2} + 2y + 1 = (y + 1)^{2}$

so the answer is

${x}^{2} - ( {y}^{2} + 1)^{2}$