Can you please show me step-by-step instructions on how to compute the wedge product in the product:

-(y dx x dy) (x³ dx + y³ dy) of differential 1-forms on R² . I need to learn how to express it in the form f dx dy where f is a function from R² to R.

and

The wedge product (2y² z dx + xyz dz) (cos(xy)dx + sin(yz)dy + e^x^2 dz) of differential 1-forms on R³. Please show me how to put the answer in form P dy dz + Qdz dx + Rdx dy where P,Q,R are functions from R³ to R.

* the above e^x^2 is e^{x where the x is squared}

^thanks