Factorise the following:- x^2-1-2y-y^2
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Factorise the following:- x^2-1-2y-y^2
If do not know the answer no need to post...
No spammers!!!!!
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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)
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:)