How to convert a function of $x$ and $y$ into a function based in polar coordinates?

Question

How did my teacher get from $x^2(x^2+y^2)$ to $r\cdot r^2\cos^2(\theta)(r^2)$?

I'm looking into the equations put I'm still at a loss because those usually require just $x$ and $y$ values like R being equal to:

$r = \sqrt{x^2+y^2}$

Thanks in advance.

Answer 1

From the definition of polar coordinates, we have that $x=r\cos(\theta)$ and $y=r\sin(\theta)$, can you take it from here?