I know how to factor out $\prod_{i=1}^{n} (a_nx_n+b_n)$ , but is there a way to reverse the process to get that product from $$a_0x_0+a_1x_1+a_0a_1x_0x_1+\cdots+\prod_{m=0}^{n}a_mx_m$$
I have 9 sets of $(ax+b)$ and need to be able to use decimals and functions eg. $\sinh(a_0a_1)x_0x_1+\cos(b_0b_2)x_0x_2...$ where $a_n$ and $b_n$ are real, and $x_n$ is a non-real constant including, but not limited to $i^2=-1$, $j^2=1$, $\lambda^{1/2}=-1$, and $\epsilon^2=0$ For the solution, I am fine with assuming symmetry of the product (or assuming all $a_n,x_n\in\Bbb{R}$). I will be able to find exceptions and changes in rules. (eg. not allowing $(-1)^2$ to be assumed as 1)