Question

x-y-x^2+y^2 factorise
​

Answer 1

Question:

x-y-x²+y² factorise.

Given:

x-y-x²+y²

To Find:

• Factorization of x-y-x² + y²

Solution:

Identity = a² - b² - ( a - b ) ( a + b )

• a = x
• b = y

=> x² - y² ( x - y ) ( x + y )

=> ( x - y ) ( 1 - ( 1x + y ) )

=> ( x - y ) ( 1 - x + y )

Answer 2

Question:

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

Solution:

Identity : a²-b²= (a+b) (a-b)

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

$\implies \: x - y - (x {}^{2} - y {}^{2} )$

$\implies \: x - y - (x + y)(x - y)$

$\implies \: 1(x - y) - (x + y)(x - y)$

$\implies \: (x-y) (1 - (x + y)$

$\implies \: (x-y)(1-x+y)$

Hence, the factorisation of x-y-x²+y² = (1-x-y)(x-y)

or we can write it as (x-y)(1-x-y)

Here, we are done :D

Related Additional Information :

We know that (x+a)(x+b) = x² +(a+b)x + ab.

Therefore, the factors of x² + (a+b)x + ab are (x+a) and (x+b)

To , identify any factor of any given question we need to find factors and if factors match then we can say that the question is factorise.