x^2-xy+x-y
\(=\left(x^2-xy\right)+\left(x-y\right)\)
\(=x\left(x-y\right)\)\(+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right)\)
x^2-4x^2+4-y^2
\(=-3x^2-y^2+4\)
x^2-4x^2+4x
\(=-1\left(3x-4\right)x\)
x^2+2xy+y^2-z^2
\(=\left(x^2+2xy+y^2\right)-z^2\)
\(=\left(x+y\right)^2-z^2\)
\(=\left(x+y-z\right)\left(x+y+z\right)\)