How can I show that the following function is homothetic? [duplicate]

$y= (x_1x_2)^2-x_1x_2$

Let $x_1x_2=z$

then $y=z^2-z$ and $y'=2z-1$

If I can prove that y' is monotonically increasing, does that prove y is a homothetic function? if so then how can I prove that y' is monotonically increasing?

marked as duplicate by luchonacho, Giskard, Herr K., Alecos Papadopoulos, BayesianJun 22 '17 at 8:31

• I added the specific point of my confusion. – xyz Jun 9 '17 at 12:01

For $x_1x_2 = y$, take then $f(y) = y^2 - y$.
If $f(y)$ is homogenous of degree $k$, it means that $f(t y) = t^k f(y)$, $\forall t>0$. In this case,
$f(t y) = (t y)^2 - t y = t^{2} y^2 - t y \neq t^k y^2 - t^k y = t^k (y^2 - y) = t^k (f(y))$