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