Factorize of the following expressions x-y-x^2+y^2 - Vidyadip

Question

Factorize of the following expressions
$x-y-x^2+y^2$

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Answer

$x-y-x^2+y^2$
$=(x-y)+\left(y^2-x^2\right)$
$=(x-y)+(y+x)(y-x)$
$=(x-y)-(y+x)(x-y)[\text { since, }(y-x)=-(x-y)]$
$=(x-y)[1-(y+x)$
$=(x-y)(1-x-y)$

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