This is your own source - and it says, juxtaposition is just multiplication
inside brackets. Don't leave out the inside brackets that they have specifically said you must use - "Parentheses must be introduced"! 🤣 BTW, this is a 19th Century textbook, from before they started calling them PRODUCTS 🙄
E=mc2 is E=(mc)2
No, it means E=mc² is E=mcc=(mxcxc)
Throwing other numbers on there
I have no idea what you're talking about 🙄
You realize a calculator doesn’t need to be a dedicated hardware, right?
You realise the calculator manufacturers have much more riding on their calculators being correct, right? 😂
Windows calculator, MacOS calculator, Android calculator, and all web-based calculators count as well.
Nope. Programmed by... programmers, who aren't earning any money from the calculator, and put the corresponding amount of effort into it.
You have no clue what you’re talking about.
says someone who just claimed that e-calcs count as much as actual, buy from a store, calculators 🤣
Alpha is a commercial product (with a free-tier as is usual nowadays)
Also well known to give wrong answers
uses the same engine as Mathematica, which is used extensively in industry, academic institutions
Nope! Academia warns against using it
None of your sources has exponents in them
In other words, you're admitting to trying to deflect from what's in Maths textbooks! 😂
that’s very convenient for your mistake of mixing up juxtaposition and your invented rule
It's the same rule, duh! Here it is in a textbook from more than 100 years ago when everything was still in brackets...
We've since then dropped the brackets from Factors which are a single Term. i.e. (a)(b+c) is now a(b+c), and (a)(b) is now ab. BTW would you like to explain how "my invented rule" appears in a textbook from more than 100 years ago? 🤣
Btw, ask yourself this as well: why would your invented interpretation of distributive law be necessary at all?
It's not invented, it's required as the reverse rule to Factorising, duh 😂 And I don't need to ask myself - as usual, all you have to do is look in Maths textbooks for the reason 😂
It brings no benefit to the table at all.
Being able to reverse the process of Factorising brings no benefit to the table?? 🤣
Juxtaposition arguably does
It's the same thing duh 🤣 ab=(a)(b), a(b+c)=(a)(b+c) notice how they are the same thing, expanding BRACKETS?? 🤣
Maybe you've forgotten about FOIL...
Now, think carefully about this, what happens when b=0, and what happens when d=0, you got it yet?? 🤣
because it allows shorter notation
AKA Factorised Terms and Products 😂
your invention doesn’t.
Again, explain how "my invention" appears in textbooks that are more than 100 years old. I'll wait 🤣
because it’s the only correct answer
Have you noticed yet that everything you think is correct is actually wrong as per Maths textbooks?? 🤣
I’ll consider your argument defeated
says person who has been comprehensively defeated by Maths textbooks and is now trying to deflect away from that 🤣
ignore further engagement from your part
I'll take that as an admission that you're wrong then, having been unable to debunk any Maths textbooks. See ya
Here you go
Yep, that's an old Casio model, Mr. "All modern calculators", proving yet again that you can't back up your own statements 😂
Please post a source that gives a different answer to this expression, I’ll wait.
No need to wait - just scroll back through this thread and look at all the sources I already posted 🙄
for big monetized products that’s no longer the case
You know none of the calculators you're referring to are commercial right? They're all free to use, and that tells you how much effort was put into them. The only e-calc I've ever seen give a correct answer is MathGPT, which is indeed commercial now (I tried it before it went commercial), so we have a commercial e-calc giving the correct answer, and all the free ones giving the wrong answer 😂
I’m in the software industry myself
So am I in case you didn't notice 😂
you have multiple downvotes in many posts
I've never seen more than 2 on any, Mr. Needs To Exaggerate Because Has No Actual Evidence Of Being Right 😂
you’re reading them wrong
says the person who is actually reading them wrong, who is unable to cite any example of me reading it wrong
clearly says a number next to a bracket means the content of the bracket must be multiplied with said number
the content of the bracket - you just quoted that yourself and still completely missed what that means 😂
Nowhere there does anybody speak of distribution taking precedence over other operations
BRACKETS has precedence over everything 😂 So here we have an example of you reading it wrong
nowhere in all sources I can find does it say so
And can you find any source which says Multiplication takes precedence over Brackets? No. Another example of you reading it wrong
Wonder why all screenshots you post use convoluted wording
They don't use "convoluted wording"! 🤣
"the contents OF THE BRACKETS should be multiplied"
"everything IN THE BRACKET should be multiplied by that number"
Yet another example of you reading it wrong 😂
wonder why you pop up everywhere arguing the same thing and keep getting downvoted?
The only person downvoting me is the person replying, whereas the others are getting downvoted by others as well 🙄
At some point you need to understand that if one old-ass calculator
My brand new Casio calculator gives the same answer! 😂 They all do now, except for Texas Instruments - the only one stubbornly still doing it wrongly
selective reading of cherry picked passages
Sure, I'm "cherry picking" the sections of textbooks about Distribution. Do you want me to post something random about a different topic? 😂 BTW, noted that you haven't come up with any textbooks that agree with you
all the proof you have
And it is indeed proof.
when all modern calculators
Agree with me (except for Texas Instruments)
algebra solvers
Written by programmers who have forgotten the rules of Maths, and as pointed out by many people in forums.
maybe it’s time to reconsider
And yet, here you are not reconsidering 🙄
Juxtaposition taking precedence over other multiplications I can understand
Because BRACKETS - ab=(axb) BY DEFINITION 😂
it’s an arguable point
And is also the exact same rule 🙄
Distribution being a mandatory step
There's a reason it's called The Distributive Law
taking precedence over even exponents is just silly
BRACKETS taking precedence over Exponents is "silly"?? 🤣🤣🤣
and unfortunately wrong
BRACKETS taking precedence over Exponents is "unfortunately wrong"?? 🤣🤣🤣
What I say to that is I’ve met plenty of teachers who are wrong about things in their own fields,
You think they're wrong you mean, person who is saying Brackets before Exponents is "wrong" 🤣🤣🤣
people defining the rules of all those algebra solvers aren’t the programmers,
Yes they are! That's why they give wrong answers 😂 I told one he was wrong and he went and fixed it, being the one who had programmed it that way 🙄
as you’d know if you looked a bit into product development.
I know they are because I have spoken directly to them 😂 Maybe try asking some yourself, before making completely wrong statements
It’s domain experts
No it isn't, as proven by personal experience. You know who uses domain experts? calculator manufacturers. 😂 They have considerably more riding on it being right or not.
who also define tests and receive feedback on the software’s performance and errors
You know there's a whole bunch of programmers who don't bother even defining tests to begin with, right??
I’m sure (lol) you’ve sent feedback to them
Yep!
they probably looked at it and decided you’re wrong
Except for the ones who did change it. The ones who claimed I was wrong, quoted Google - who have also been told they're wrong by many people -and not Maths textbooks 🙄
As well all have.
says person who did nothing of the sort, and lied about such things as "all modern calculators " being against me (they aren't, if you had actually tried some), Exponents having precedence over Brackets, etc.
Dude you’re not even hitting the right reply buttons anymore
Yes I am
Is that what you do when you’re drunk?
Is that why you think I'm hitting the wrong buttons?
It’d explain leading with ‘nope! I’ve said exactly what you accused me of.’
I have no idea what you're talking about. Maybe stop drinking
You keep pretending distribution is different from multiplication
No pretending - is is different - it's why you get different answers to 8/2(1+3) (Distribution) and 8/2x(1+3) (Multiplication) 😂
B 8/2(1+3)=8/(2+6)=8/8
E
DM 8/8=1
AS
B 8/2x(1+3)=8/2x4
E
DM 8/2x4=4x4=16
AS
That’s not Multiplication, it’s Distribution, a(b+c)=(ab+ac), a(b)=(axb).
That's right.
And then posting images that explicitly say the contents of the brackets should be multiplied
The "contents OF THE BRACKETS", done in the BRACKETS step , not the MULTIPLICATION step - there you go quoting proof that I'm correct! 😂
Or that they can be simplified first.
That's right, you can simplify then DISTRIBUTE, both part of the BRACKETS step, and your point is?
B 8/2(1+3)=8/2(4)=8/(2x4)=8/8
E
DM 8/8=1 <== same answer
AS
I am not playing dueling-sources with you
No, because you haven't got any 😂
your own sources call bullshit on what you keep hassling strangers about
says person failing to give a single example of that EVER happenning 😂
I'll take that as an admission of being wrong then. Thanks for playing
You’ve harassed a dozen people to say only 53+514
Nope! I've said a(b+c)=(ab+ac) is correct.
to the point you think 2(3+5)2 isn’t 2*82
You mean I know that, because it disobeys The Distributive Law 🙄 The expression you're looking for is 2x(3+5)², which is indeed not subject to Distribution, since the 2 is not next to the brackets.
If you’d stuck to one dogmatic answer
Instead I've stuck to one actual law of Maths, a(b+c)=(ab+ac).
But you’ve concisely proven
The Distributive Law, including c=0 🙄 Not sure why you would think c=0 is somehow an exception from a law
the harassment is the point
No, the rules of Maths is the point
when you can’t do algebra right
Says person who thinks c=0 is somehow an exception that isn't allowed,🙄but can't cite any textbook which says that
I think I know what you're missing - perhaps intentionally 🙄 - in a(b+c), c can be equal to 0. It can be any number, not just positive and negative, leaving us with a(b)=(axb), which is also what I've been saying all along (not sure how you missed it, other than to deliberately ignore it)
And what do you do with and and the b and then the a and the c?
BTW, there's no "the a and the b" and "the a and the c", there's ab and ac, which need to be added. If a=2, b=3, and c=4, we have 2(3+4)=(6+8)=14
The first textbook only gets 5(17) by not doing what the second textbook says to do with 5(3+14)
Because the first textbook is illustrating do brackets from the inside out, which the second textbook isn't doing (it only has one set of brackets, not nested brackets like the first one). They even tell you that right before the example. They still are both Distributing. You're also ignoring that they actually wrote 5[3+(14)], so they are resolving the inner brackets first, exactly as they said they were doing. 🙄 The 5 is outside the outermost brackets, and so they Distribute when they reach the outermost brackets. This is so not complicated - I don't know why you struggle with it so much 🙄
First image says ‘always simplify inside,’ and shows that
And then says to Distribute, and shows that 🙄 "A number next to anything in brackets means the contents of the brackets should be multiplied".
Second image says ‘everything inside must be multiplied,’ and shows that
Yep, that's right, same as I've been telling you the whole time 😂
You’re such an incompetent troll that you proved yourself wrong within the same post
Ah, no, you did, again - you even just quoted that the second one also says to Distribute! BWAHAHAHAHAHAHAHA! 😂 I'll remember that you just called yourself an incompetent troll going forward. 😂
I’ve read everything you’ve posted
You've read every textbook, and looked at the calculator answer? Yeah nah, you clearly haven't.
you’re interpreting the texts in such a way that they support your flawed argument
Says person who can't come up with any textbooks that support their argument. 😂 BTW if you had looked at the calculator, you would've seen it does it exactly as I have described - 6/2(1+2)=6/2(3)=6/(2x3)=6/6=1, not, you know, 6/2(1+2)=3(3)=9, which is your flawed argument
conveniently ignoring what they’re actually saying, such as “if” statements
Says person ignoring this "if" statement which says you literally must distribute if you want to remove the brackets.
Even this textbook that you yourself posted goes against what you’re saying
No it doesn't! 😂
Notice something?
Yes, you ignored the Distribution in the last step 😂 I have no idea what you think is significant about the first 2 steps, other than you were trying to draw attention away from the Distribution in the last step
Here's another one (different authors) that does the same thing, which you would've seen if you had actually read all the textbooks I posted, but they explicitly spell out what they're doing as they're doing it...
5(17) means they didn’t distribute 5(3+14) into 53+514
That's right, they Distributed the 5(17) into (5x17), and your point is?
These textbooks unambiguously disagree
With you, yes, and your point is?
Please find a Maths textbook that backs that up as being the correct answer. i.e. Exponents before Brackets. Should be easy, no? 🤣