Why doesn't $(x+y)^2 $equal $x^2+y^2$? I need to explain this to someone.
I know obviously the expanded form gives you $x^2 + 2xy + y^2$ but technically don't the individual exponents multiply to give $x^2 + y^2$
I might say I'm looking for an interesting geometrical explanation for this.
Any help is appreciated!

If $x=y=1$, then it should be obvious that
$$(1+1)^2=2^2=4$$
$$1^2+1^2=1+1=2$$
So it should be trivial that
$$(1+1)^2\ne1^2+1^2$$
And it cannot hold in general if it fails for at least one case.
