I apologize if the motivation wasn't clear.
At a mathematical level, it's a problem of multiplying N polynomials, each of which has two terms:
(a+b)*(c+d) = ac + ad + bc + bd
(a+b)*(c+d)*(e+f) = ace + acf + ade + adf +
+ bce + bcf + bde + bdf
What I was after was an explicit expression for
each of the 2**N
terms on the right-hand-side of these equations.
As for why one would want to do this beyond a homework
question, this problem arises in theories of
quantum computing, particularly in trying to
write an arbitrary state in terms of what's called the
computational basis for an N-qubit state.