Question about variable and constant notation in some properties I am just starting to think about mathematical notation a lot more and some parts of it do not make as much sense to me as I would like. I am operating under the convention that beginning alphabet letters are constants and ending alphabet letters are variables.

I see this equation in algebra and calculus text books: $a(b+c)=ab+ac$ 
What this means to me is that it is true for constants, but says nothing about variables. But this clearly is true for variables as well, as you can do equations such as $x^2-2x=x(x-2)$. 

Why is some math notation written this way, or rather, why isn't the property written as $x(y+z)=xy+xz$ since that would signify that it works for any unknown and not just constants. This goes for all the elementary algebra fraction equations as well. And then to make it even more confusing, as soon as exponents are involved, variables are now introduced, such as $x^mx^n=x^{m+n}$. Wouldn't a constant work just as well here? Am I just not understanding something basic about notation? 

p.s. If there is a good resource to clarify mathematical notation I would love to see it.
Of course, they are all variables. Your perception is somewhat correct in the sense that customarily constants (or, "parameters") in the context of a specific problem are often denoted $\{a,b,c,\ldots\}$. But a symbol is a symbol is a symbol. Even the symbol $\pi$ isn't always used just to mean the number $3.1415926535...$
I don't quite get you. When you say $a(b+c) = ab +bc$ is true for 'constants',  does that mean it is true not only for $a=1$, $b=2$ and $c=3$, but also for $a=5$, $b=3$ and $c=3$, and so on and so forth. So there you are, it is varying in that sense. When I have an equation, say  $y=x²+c$ then only $x$ and $y$ are varying and $c$ is fixed, but $c$ can be any 'constant'. It's not varying in the sense in which $x$ and $y$ are varying. So depends on what the context is, I suppose.