Here is math for kids https://www.mathsisfun.com/definitions/distributive-law.html
Distributive law means you are allowed to distribute, not that you must distribute. I'm so sorry for the amount of effort you're futilely putting into this lmao. Nowhere in all your sources and screenshots is it stated you must distribute, and thus the entire argument breaks down.
You must not distribute brother, lay it to rest lmao. It's optional. Google distributive law and find me one source saying it's imperative to distribute - there's none. You can even confirm this is true yourself with simple examples like the ones I've mentioned above.