Question: Expanding out polynomials subject to relations

I would like to use Maple to expand the polynomial (1+x[1]+y[1])*(1-x[1])*(1-y[1])*(1+x[2]+y[2])*(1-x[2])*(1-y[2])*(1+x[3]+y[3])*(1-x[3])*(1-y[3])*(1+x[4]+y[4])*(1-x[4])*(1-y[4]). This is dreadfully complicated, but things are simplified by the fact that (in my situation) each x[i] and y[i] disappears when squared (x[i]^2 = y[i]^2 = 0 for all i). Is there a way to make Maple factor this into the computation?

 

Cheers,

 

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