Question

factorise x-y-x^2+y^2

Answer 1

Hey!
The given equation= x-y-x^2+y^2.
=> (x-y)-(x^2-y^2)
Use the identity, a^2-b^2= (a-b)(a+b).
=> (x-y)-(x+y)(x-y)
Take x-y common
=> (x-y)(1-x-y). {Ans.}

Answer 2

The answer is -( x + y - 1) (x - y)

Given: x - y - x² + y²

To Find: The factor of x - y - x² + y²

Solution:

Evaluate

x - y - x² + y²

Rewrite the expression

-x² + xy - xy + y² + x - y  

Factor out x from the equation

-x(x - y) - xy + y² + x -y

Factor out y from the expression

-x(x - y) - y(x - y) + x - y

Factor out x - y from the expression

( - x - y + 1)(x - y)

or,  -( x + y - 1) (x - y)

∴ The solution is  -( x + y - 1) (x - y)

Hence the factor = -( x + y - 1) (x - y)

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