$x = rcosΘ$

$y = rsinΘ$

$dx = -rsinΘdΘ + cosΘdr$

$dy = rcosΘdΘ + sinΘdr$

$dxdy = (-rsinΘdΘ + cosΘdr)(rcosΘdΘ + sinΘdr) 
= -r^2sinΘcosΘdΘ^2 - rsinΘ^2drdΘ + rcosΘ^2dΘdr + sinΘcosΘdr^2$

this seems can not be simplified to $rdrdΘ $

**why?**