Question on Factoring I have very basic Question about factoring, we know that,
$$x^2+2xy+y^2 = (x+y)^2$$
$$x^2-2xy+y^2 = (x-y)^2$$
But what will 
$$x^2-2xy-y^2 = ??$$
$$x^2+2xy-y^2 = ??$$

There is no simple factorization of $x^2+2xy-y^2$ nor $x^2-2xy-y^2$, although you can write:
$$\begin{align}x^2+2xy-y^2 &= (x+y)^2-2y^2 \\&= \left(x+y(1+\sqrt{2})\right)\left(x+y(1-\sqrt{2})\right)
\end{align}$$
and similarly:
$$x^2-2xy-y^2 = \left(x-y(1+\sqrt{2})\right)\left(x-y(1-\sqrt{2})\right)$$
