Question

x^2-1-2y-y^2 factorise the following expressions​

Answer 1

Required Answer:-

Given To Factorise:

• $\tt x^{2}-1-2y-y^{2}$

Solution:

Given,

$\tt= x^{2}-1-2y-y^{2}$

This can be written as,

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

Now, let us factorise y² + 2y + 1 first.

$\tt y^{2} + 2y + 1$

$\tt= y^{2} + y+y + 1$

$\tt= y(y+ 1)+1(y+1)$

$\tt= (y+ 1)(y+1)$

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

So,

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

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

By using identity a² - b² = (a +b)(a - b), we get,

$\tt = (x + y + 1)(x - y - 1)$ which is our required answer.

Answer:

• $\tt (x + y + 1)(x - y - 1)$

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