I am trying to recall math from many years ago (for me). I am trying to figure out how to multiply out the matrices for trilateration. If you could look here: https://www.ece.lsu.edu/scalzo/FDR_Final.pdf - on page 12, I am talking about Equation 6 and Equation 7 - the equations to get the coordinates.
My question is...how do I multiply the polynomials together correctly. Am I supposed to evaluate them how they are in their position, and then cross multiply the results? Or is it more complicated...like the opposite of factoring (again I'm hazy on my math). If you could provide an example for how to do one of the matrices that would be great. Thanks.
UPDATE
Essentially, I want to know how to handle the multiplication like (a-b)-(c-d)-(e-f) * 2(g-e)...do I handle the 3 subtractions in parenthesis on the left side of the * before I multiply? or do I have to multiply the 2(g-e) by each polynomial and factor in all of the signs?
Either way, for example the numerator of $\,(6)\,$ is:
$$ \left| \begin{matrix} (a-b)-(c-d)-(e-f) & 2(g-h) \\ (a'-b')-(c'-d')-(e'-f') & 2(g'-h') \end{matrix} \right| \\[5px] = \Big((a-b)-(c-d)-(e-f)\Big) \cdot 2(g'-h') - \Big((a'-b')-(c'-d')-(e'-f')\Big) \cdot 2(g-h) \\[5px] = 2\,\Big((a-b)(g'-h')-(c-d)(g'-h')-(e-f)(g'-h')\Big) \\ \; -2\,\Big((a'-b')(g-h)-(c'-d')(g-h)-(e'-f')(g-h)\Big) $$
Which one to choose depends on computational considerations rather than math ones.