I am producing a short article.
In mathematical writing, does it make sense to put a single numbering on an equation that has two or more arrangements?
For example, does it make sense to write: given $x,u$ vectors, $A,B$ square matrices of equal dimension
$$ \begin{equation} x = BABu = AB^2u \quad \quad \quad (1) \end{equation} $$
or should I write
$$ \begin{equation} x = BABu \quad \quad \quad (1) \end{equation} $$
or
$$ \begin{equation} x = AB^2u \quad \quad \quad (1) \end{equation} $$
The intention is to show the user that there exists multiple arrangements which may all be enlightening. However, is I write $$ \begin{equation} x = BABu = AB^2u \quad \quad \quad (1) \end{equation} $$ would it cause confusion as to which form of $x$ is $(1)$ is specifically referencing?
Can someone comment on this etiquette
If you insist on using the notation where you split the lines to show different versions of the same thing, consider making the second incidence primed to distinguish them as in the following:
\begin{equation} x = BABu \quad \quad \quad (1) \end{equation} or \begin{equation} x = AB^2u \quad \quad \quad (1') \end{equation}
This way you can reference both forms if you need to without ambiguity, but you don't need to increase the equation index.
Also note that matrix multiplication isn't commutative in general, so be careful when writing something like $BABu = AB^2u$ because it isn't always true.