Here you go:
Please post a source that gives a different answer to this expression, I'll wait.
There's of course programmers that implement their own projects, but for big monetized products that's no longer the case. I'm in the software industry myself and have worked extensively in product development.
Sure bro you have multiple downvotes in many posts, I'm sure it's the person you're arguing with logging in with multiple accounts lol.
Yep I have looked at all you've posted, I say you're wrong because what you've posted says things that are true, but you're reading them wrong. For example your last image clearly says a number next to a bracket means the content of the bracket must be multiplied with said number. Nowhere there does anybody speak of distribution taking precedence over other operations. In fact, nowhere in all sources I can find does it say so. Wonder why all screenshots you post use convoluted wording and wonder why you pop up everywhere arguing the same thing and keep getting downvoted? At some point you need to understand that if one old-ass calculator and selective reading of cherry picked passages is all the proof you have, when all modern calculators and algebra solvers go against you, maybe it's time to reconsider.
Juxtaposition taking precedence over other multiplications I can understand and it's an arguable point. Distribution being a mandatory step and taking precedence over even exponents is just silly and unfortunately wrong.
Also another thing: you're a math teacher as you've said, and consistently ask if I think "random programmers" know more about algebra than you. What I say to that is I've met plenty of teachers who are wrong about things in their own fields, for one. And also, people defining the rules of all those algebra solvers aren't the programmers, as you'd know if you looked a bit into product development. It's domain experts, who also define tests and receive feedback on the software's performance and errors. I'm sure (lol) you've sent feedback to them, and they probably looked at it and decided you're wrong. As well all have.
I've read everything you've posted, but the problem is you're interpreting the texts in such a way that they support your flawed argument, conveniently ignoring what they're actually saying, such as "if" statements.
Even this textbook that you yourself posted goes against what you're saying if you just bother to look at it outside of your tunnel vision:
Notice something?
Lmao citing yourself and assuming you're correct and smarter than everyone who programs solvers, even those who are known to be respectable and used extensively in academia. Nothing's been established cause you've cited sources that don't support your argument, and repeating them again and again won't make it different. Good day bro, continuing this is useless.
Ok bro now find an expression solver that verifies your solution. I tried Wolfram Alpha, Google, and others, and they all return 128. So either you're wrong, or all people who make these tools professionally are wrong. Not trying to be offensive, but I know where I'm putting my money.
To be clear, the reason you're wrong is because distribution is not part of the brackets step. Brackets are solved before exponents, resulting in 2(8)². Remove the brackets and then it's 2*8²
Exponents come after brackets, so I'm curious to see how you solve that with your logic lol. It has an obvious correct solution, which is 128, but you need to distribute in the brackets step, which comes before exponents, so let's see what you do with it lmao.
Ok bro so answer my question what's the result of the expression I wrote above?
Bro directly after what you underlined it says "if you want to remove the brackets" lol. Selective reading much? "If" means optional. You are free to solve what's inside the brackets first, before multiplying it with what's outside.
Also, the link I posted is literally titled "distributive law", not property. You realize a law can have conditions, right?
Quick quiz for you: what's the result of 2(3+5)² ?
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.
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.
Nowhere in your "proof" screenshots does it say anything about distribution being part of the brackets step. Distribution is a method that can help solve equations, but it isn't required. If you have 2(3+5) you're free to solve it as 2*3+2*5 or as 2*8, whichever is easiest. That is because juxtaposition means multiplication and nothing else.
Math textbooks almost universally will either use clear brackets or simply write divisions in 2 lines, which avoids the confusion altogether.
You realize a calculator doesn't need to be a dedicated hardware, right? Windows calculator, MacOS calculator, Android calculator, and all web-based calculators count as well.
You have no clue what you're talking about. Wolfram Alpha is a commercial product (with a free-tier as is usual nowadays) and uses the same engine as Mathematica, which is used extensively in industry, academic institutions, and government agencies.
None of your sources has exponents in them, and that's very convenient for your mistake of mixing up juxtaposition and your invented rule.
Btw, ask yourself this as well: why would your invented interpretation of distributive law be necessary at all? It brings no benefit to the table at all. Juxtaposition arguably does, because it allows shorter notation, but your invention doesn't.
Please find a calculator that gives a result different to 128 for the expression
2(3+5)². You won't be able to, because it's the only correct answer. If you don't post a reproducible example of a solver anywhere coming to a different solution, I'll consider your argument defeated and ignore further engagement from your part. Have a nice day!