How to factorise this expression $ x^2-y^2-x+y$ This part can be factorised as  $x^2-y^2=(x+y)(x-y)$, How would the rest of the expression be factorised ?
:)

This is a far less elegant method than the other answers but I'll keep it up for posterity: set it up as a quadratic in $x$.
$$x^2-x+(y-y^2)=0$$
$$x=\frac{1\pm\sqrt{1+4(y^2-y)}}{2}$$
$$\left(x-\frac{1+\sqrt{1+4(y^2-y)}}{2}\right)\left(x-\frac{1-\sqrt{1+4(y^2-y)}}{2}\right)$$
$$\frac{1}{4}\left(2x-1+\sqrt{(2y-1)^2}\right)\left(2x-1-\sqrt{(2y-1)^2}\right)$$
$$\left(x+y-1\right)\left(x-y\right)$$
