Question

Factorise the following:- x^2-1-2y-y^2
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Answer 1

Answer:

(x — y — 1)(x + y + 1)

Step-by-step explanation:

Rearrange the terms as follows:

x^2 — y^2 — 2y — 1

Group the last three terms, factoring out a —1:

x^2 — (y^2 + 2y + 1)

Those last three terms are a perfect square:

x^2 — (y + 1)^2

Now you have the difference of two squares:

[x — (y + 1)][x + (y + 1)]

Remove the inner grouping symbols to get

(x — y — 1)(x + y + 1)

Answer 2

x² - 1 - 2y - y²

= x² - y² - 2y - 1

= x² - ( y² + 2y + 1 )

= x² - ( y + 1 )²

= [ x + ( y + 1 ) ] × [ x - ( y + 1 ) ]

= [ x + y + 1 ] × [ x - y - 1 ]

Hope it helps:)