Doubt in using $dx\wedge dy$

Question

In my class notes there was this question to show that $d^2f=dy\wedge dx(f_{yx}-f_{xy})$, i did mannaged to find the correlation as follows $$d^2f=d(dxf_x+dyf_y)=dx\wedge df_x+dy\wedge df_y$$ $$=dx\wedge (dxf_{xx}+dyf_{xy})+dy\wedge (dxf_{yx}+dyf_{yy})=dx\wedge dyf_{xy}+dy\wedge dxf_{yx}$$ and because $dx\wedge dy=-dy\wedge dx$ I can find $dy\wedge dx(f_{yx}-f_{xy})$. My doubt is more of a curiosity, can i day that$$dx\wedge dy(...)=(...)dx\wedge dy$$ or is there a convention against it?