\(x^2-y^2+x-y\)
\(=\left(x+y\right)\left(x-y\right)+\left(x-y\right)\)
\(=\left(x+y+1\right)\left(x-y\right)\)
\(x^2-y^2+x-y\)
\(=\left(x^2-y^2\right)+\left(x-y\right)\)
\(=\left(x+y\right)\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y+1\right)\)
\(x^2-y^2+x-y\\ =\left(x-y\right)\left(x+y\right)+\left(x-y\right)\\ =\left(x-y\right)\left(x+y+1\right)\)