$\lim _{n\to \infty }\left(\left(1+\frac{x}{n}\right)^2+\left(\frac{y}{n}\right)^2\right)^{\frac{n}{2}} = e^x$ - how to prove?

Question

$\lim _{n\to \infty }\left(\left(1+\frac{x}{n}\right)^2+\left(\frac{y}{n}\right)^2\right)^{\frac{n}{2}} = e^x$
I saw at wolfram that the limit is equal to $e^x$, but could not prove it.. I tried maybe doing common factor of $\left(1+\frac{x}{n}\right)^2$ By doing so, I could get that common factor out of the brackets, but I get another problem by doing that...
$\lim _{n\to \infty }\left(\left(1+\frac{y}{n+x}\right)^2\right)^{\frac{n}{2}}$, I get left with that limit and it is equal to $e^y$. Thus I receive at the end $e^{x+y}$ which is not the desired limit...

I thought also of using arithmetic's, by calculating the limit separately, but it will not work also.. Any ideas will be much appreciable!!
(This is to proof Euler limit of $e^z$, but with hints I was given, saw other topics, none related, I need to use my hints which is the post basically, in the two hints I am stuck with the same thing, in this case the $e^y$

EDIT: David Mitra helped me find the solution, apparently at line 5, I didnt notice myself, but I did square brackets on all, which is my mistake. Thanks!! if anybody else sees this post, I got the solution :)