How to calculate wedge product of differential forms Consider the differential forms on $\mathbb{R}^3$, 
$\omega_1 = xy \space dx + z \space dy + dz$ ,  $\omega_2 =  x \space dy + z \space dz$. 
I need to determine $\omega_1 \wedge \omega_2$. 
However, I do not know how to find such wedge products. Any help is appreciated. 

$$ \sum_I a_I dx^I \wedge  \sum_J b_J dx^J: = \sum_{I, J} (a_I b_J)\  dx^I \wedge dx^J$$
$\textbf{Example}$:
$$(x dx + y dy) \wedge (2 dx - dy) = 2x  \ dx \wedge dx- x \ dx \wedge dy + 2y \ dy \wedge dx- y \ dy \wedge dy\\ \hspace{-.41in}= (-x-2y)\  dx \wedge dy$$
