I wasn't going to reply any more, but I see now you don't understand terms either, so one more time for old time's sake (and maybe you might finally get it)...

perhaps you have sunk so much time

You know teachers don't get paid for helping students outside class time right?

assume I must be wrong

No assumption needed. What you are proposing is literally impossible. I've been saying that all along.

Take another look at my third and fifth paragraphs.

Ok...

I’m not saying you can take any expression and get the same answer by doing addition before multiplication

And so far you haven't been able to show it works for any expression at all! Not even one expression! Just like I said would happen.

All I am saying is that you can still use numbers to solve problems with an altered order of operations

And I said you can't, and you haven't! All you did was put brackets around the multiplication to make sure we were still following the only order of operations that works! You have still not shown an actual instance where one can actually do addition first and get a right answer, not one! The idea that one could use addition first as an "alternate order of operations" is thus pure fantasy, just like I've been saying all along. It's literally impossible.

for example (x+4)(x-2) would no longer need brackets

Yes it would! (x+4) is one term - that's what the brackets means - "these things are all together". If you remove that, because "addition first", it's now two terms, so the whole expression is two terms (instead of one), x, and 4(x-2) (which is a mistake people make when they write 8/2(2+2) as 8/2x(2+2) - just turned 2 terms into 3 terms and changed the answer!). Every example you've done so far you've used brackets to escape from having to do addition first, and the very same thing would therefore apply here - no brackets, no escaping "addition first" approach, brackets before addition leads to x+4(x-2)=x+(4x-8) =5x-8, which is not the product of (x+4) and (x-2).

The presence of brackets where there would be none otherwise does not invalidate my point

No, the fact that you've not been able to show a single instance of where addition before multiplication would work does. You can't show "a way to solve this in an addition first world" when it's literally impossible for an "addition first world" to exist in the first place.

I never wrote 15²+50²

...and I removed the brackets to show that addition first doesn't work (since you keep putting in brackets to revert "addition first" back to the only order of operations that actually works).

It can still be used to “study of the measurement, properties, and relationships of quantities and sets using numbers and symbols”

And you've still not shown how. Every example you've used so far you've put in brackets to your (supposed) "addition first" so that we were evaluating it using the only order of operations that works. In other words, no, you can't use "addition first" to “study of the measurement, properties, and relationships of quantities and sets using numbers and symbols” - you used the regular order of operations to do it! You haven't shown a single example of where addition first could be used to do it.

you need to use that order of operations

You need to use an order of operations that gives a correct answer, of which there is only one - a fact you keep trying to avoid.

different order of operations and a+2xa-2 simplifies to a^2-4

No it wouldn't, cos now you're ignoring terms as well. As per my earlier working out, it would simplify to 5x-8 unless you also changed the definition of terms. Do you see yet why it's impossible to have an "alternate order of operations"?

All I am trying to say is that that their math, with a different order of operations, would be no less useful then our math

And you've completely failed to show a single instance where this is true - which is what I've been saying all along, it's impossible to have another set of order of operations that works. You keep pre-supposing it's possible, but then add brackets to the multiplications so that we follow the actual correct order of operations, the only order of operations that works.

my only claim is that you can still use a different order of operations to manipulate numbers and solve real world problems

And you've still failed to solve a single problem using addition first, because it's still a fact it's literally impossible to do so.

was still able to come to the correct answer

by using the only order of operations that works. i.e. multiplication before addition.

Now I really am done - I'm not going any further down this rabbit hole of whatever other Maths you may not understand either (this post it was Terms - who knows what's next)...