Solve for: x^2-y^2+x-y

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

Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression

$\left( x-y \right) \times \left( x+y \right)+x-y$

Factor out $x-y$ from the expression

$\left( x-y \right) \times \left( x+y+1 \right)$