<s>[INST] If $x+y$ is a factor of $x^2$ prove it's also a factor of $y^2$ If $X+Y$ is a factor of $X^2$ prove $X+Y$ is a factor of $Y^2$.
I have tried the rmainder theorem, attempted factorisation but those don't work.
 [/INST] $x,y$ and $k$ are integers.
$x^2=k(x+y)$;
$((x+y)-y)^2=$
$ (x+y)^2-2y(x+y)+y^2=k(x+y);$
$y^2=k(x+y) -(x+y)^2 +2(x+y)y;$
Hence?
</s>