Consider the infinite product

(1-qⁱ)(1-qⁱz^-1)(1-q^i-1z)

For i > 0

How would I expand this into a power series in qz in Maple? Say I would like the coefficient of q⁶z²

Or how would I get the first n terms up to some order of qz?

How can one find the number of real solutions of a polynomial, when the polynomial is depending on a parameter. For instance, gven the following polynomial

x^4-2x^3-x^2+8x+8-2t

for t in the reals

How can I find the number of real solutions? I know you can use solve(..., reals), if the polynomial wasn't parametrized, but can maple take the parameter into account?