PDFs found online

Nope! If you looked more carefully you'll find some of them are photo's and scans. You also seem to be forgetting that every modern textbook comes with a PDF as well 🙄

From which you are ignoring counterexamples using a(b+c)n. Fraud

says the actual fraud who keeps ignoring that there is no exponent in a(b+c) 😂

Go ahead and tell me how you would explain what 3(x+y) means without referring to Multiplication?

Your own spammed screenshots say 3 gets multiplied

So in other words, you weren't able to. Also, it doesn't say that - well done on missing the point for a third time in a row 😂

There is no special case

So you think 2(3x4x5)=(2x3x2x4x2x5) is totally fine? BWAHAHAHAHAHAHAAHA 😂😂😂

You made it up

Weird then that it's in Maths textbooks isn't it, that 2(3x4x5) is in fact only equal to 2(60)? 😂

does it just mean 8?

says person showing they don't know the difference in meaning between "means" and "equals" 😂

so 2(8+0)2 is the same as 2(8)2

Yep.

The latter is the next step in simplifying the former

Yep.

You’ve admitted simplifying first is valid

Yep.

when your nose was rubbed in your own found PDFs doing exactly that

Nope! When you finally discovered that they were both valid, even though only a couple of textbooks I posted specifically said to Distribute first. We in fact teach students to simplify before Distributing - less working out, less mistakes with signs.

You don’t have an opinion

That's right, just facts, as per Maths textbooks 😂

You make no claim, anymore

a(b+c)=(ab+ac), same thing I've been saying the whole time

All you have left are derision and emojis

and facts

You’ve admitted 2(8*1)2 means 2(8)(8)

Nope! Never said anything of the sort, liar. I have said the whole time that Multiplication is a special case, to which you claimed there was no special case.

insist that’s different from 2(8)2 because…

No Multiplication. It's not complicated 🙄

You cannot explain it even now

I already did. Not my fault you don't understand the difference between Addition and Multiplication 😂

Your bullshit hit max comment depth.

That's hilarious that you're calling textbooks "bullshit" 🤣🤣🤣 BTW there's nothing preventing you from addressing comments made in a different post to the one you're replying to, 🙄 and yet, yet again, you didn't. Did you work out yet why we don't write (a+b)c? It's all in the post you're avoiding.

So when you said 2(8)2 is 256, you were wrong

Nope. 2(8*1)² has a Multiplication inside the Brackets, so The Distributive Law does not apply, 2(8)² doesn't have Multiplication in it, so The Distributive Law does apply. As I've already said repeatedly, if you wanted 2x8², then you could've just written 2x8². If you've written 2(8) rather then 2x8, then you are saying this is a Product, not a Multiplication.

Otherwise - walk me through how 2(8*1)2, 2(8+0)2, and 2(8)2 aren’t equal, alleged math teacher.

I already did multiple times. The first one has Multiplication in it, the other two don't. Multiplication (and Division) is the special case where The Distributive Law does not apply, because you cannot Distribute over Multiplication, only Addition (and Subtraction)

alleged math teacher.

who mysteriously owns dozens of Maths textbooks, many of which quoted in the post you're avoiding 😂

None of them have said a(b+c)=ax(b+c)

“3(x+y) means 3*(x+y).”

Yep, doesn't say equals, exactly as I said 🙄 Congratulations on missing the point a second time in a row. You wanna go for three?

“It depends on what the definition of is, is,”

You think "means" and "equals" are the same word?? BWAHAHAHAHAHAHA! 🤣🤣🤣 You know the language has to get dumbed down to Year 7 level, right? And you're still missing the point, right? 😂 Go ahead and tell me how you would explain what 3(x+y) means without referring to Multiplication? I'll wait. BTW I'll point out yet again That the questions on Page 282, answers on Page 577, prove I am the one interpreting this right. Maths teacher understands Maths textbook language better than someone who isn't a Maths teacher. Who woulda thought?? 😂

says someone definitely not trapped in a contradiction

Yep, I'm definitely not trapped in a contradiction. 🤣🤣🤣 Look at the questions on Page 282, answers on Page 577, and then ask yourself what you think they meant when they said means, 😂and not equals. There is definitely a specific reason they did not say equals

Firstly, it's hilarious that you've gone back to a previous comment, thus ignoring the dozen textbook references I posted 😂

That would mean 2(8*1)2 is 128

That's right, because we don't Distribute over Multiplication (and Division), only Addition and Subtraction (it's right there in the Property's name - The Distributive Property of Multiplication over Addition). Welcome to you proving why a(bc)² is a special case 😂 I've been telling you this whole time that a(b+c) and a(bc) aren't the same, and you finally stumbled on why they aren't the same 😂

You are the one saying it’s not 2a2b2,

No I'm not. I never said that, liar. I've been telling you the whole time that it is a special case 🙄 (upon which you claimed there was no special case)

because you think it’s 22a2b2,

No I don't. That's why you can't quote me ever saying that 🙄

exponents are where you are blatantly full of shit

and there are no exponents in a(b+c) and all this stuff about exponents is you being blatantly full of shit 🙄

Source: your ass.

No, this meme

Notice that there are no exponents? 😂

Every published example disagrees

says person who came back to this post to avoid this post which is full of published examples that agree with me - weird that 😂

that up-to-date Maths textbook must be wrong

And I also pointed out why that was wrong here. i.e. the post that you have avoided replying to 😂

You alone are correct on this accursed Earth

No, all textbooks as well, except those which are using the old-fashioned and wrong syntax of (a+b)c, not to mention most calculators as well (only Texas Instruments is still doing it wrongly).

Page 31 of the PDF… right

Before the pages I already posted in the post that you are avoiding replying to 😂

where you’ve dishonestly twisted the “expanding brackets” text. Next page: “3(x+y) means 3*(x+y).”

means not equals, Mr. Person Who Is Actually Dishonestly Twisting The Words, as proven by the exercises on Page 282, answers on Page 577, which are also in the post that you are avoiding replying to 😂

Page 129 of that PDF, exercise 5, question 14: simplify 2(e4)2. The answer on PDF page 414 is 2e8

That's right

Your bullshit would say 4e8.

Nope. Been telling you the whole time that is a special case, upon which you claimed there was no such special case 😂

if you somehow need further proof of how this actually works

No, I don't, it's still a False Equivalence argument 🙄 But if you wanna waste your time on an irrelevant point (which you seem determined to do), go ahead, don't let me stop you, but that's an admission that you are wrong about a(b+c)

Damn dude, that’s five textbooks you chose saying you’re full of shit

Nope! None of them have said a(b+c)=ax(b+c), they have all said a(b+c)=(ab+ac), which is why you're avoiding replying to the post of mine which quotes them all 🙄

This is a college textbook, and that explains how to solve it

It's a college refresher course on high school Maths. They also forgot to cover The Distributive Law, which is not unusual given college Professors don't actually teach high school Maths.

Another example

From the same refresher course 🙄

Alternatively, here is another example

Which also doesn't cover The Distributive Law, which isn't surprising given that chapter isn't even about order of operations! 😂

In case you can’t find the correct part

Still not about a(b+c). You lot are investing so much effort into such an obvious False Equivalence argument it's hilarious! 😂

Solving brackets does not include forced distribution

Yes it does! 😂

Juxtaposition means multiplication,

No, it doesn't. A Product is the result of Multiplication. If a=2 and b=3, axb=ab, 2x3=6, axb=2x3, ab=6. 3(x-y) is 1 term, 3x-3y is 2 terms...

as such, 2(3+5)² is the same as 2*(3+5)²

No it isn't. 2(3+5)² is 1 term, 2x(3+5)² is 2 terms

so once the brackets result in 8

They don't - you still have an undistributed coefficient, 2(8)

they’re solved

Not until you've Distributed and Simplified they aren't

Distribution needs to happen if you want to remove the brackets

if you want to remove the brackets, YES, that's what the Brackets step is for, duh! 😂 The textbook above says to Distribute first, then Simplify.

while there are still multiple terms inside

As in 2(8)=(2x8) and 2(3+5)=(6+10) is multiple Terms inside 😂

it’s still a part of the multiplication

Nope! The Brackets step, duh 😂 You cannot progress until all Brackets have been removed

which has higher priority.

It doesn't have a higher priority than Brackets! 🤣

Your whole argument hangs on the misinterpretation of textbooks

says person who can't cite any textbooks that agree with them, so their whole argument hangs on all Maths textbooks are wrong but can't say why, 😂 wrongly calls Products "Multiplication", and claimed that I invented a rule that is in an 1898 textbook! 🤣 And has also failed to come up with any alterative "interpretations" of "must" and "Brackets" that don't mean, you know, must and brackets 😂

This is what it feels like to argue against Bible fanatics

says the Bible fanatic, who in this case can't even show me what it says in The Bible (Maths textbooks) that agrees with them 😂

provide me a solver that says 2(3+5)² is 256 and you’ve won, it’s so easy no?

provide me a Maths textbook that says 8/2(1+3)=16 and you’ve won, it’s so easy no? 🤣

And in the meantime, here's one saying it's 1, because x(x-1) is a single Term...

Nobody has argued exponents should go before brackets

You did! 😂 You said 2(3+5)²=2(8)²=2(64), which is doing the Exponent when there are still unsolved Brackets 😂

I’m saying distribution being mandatory is an invented rule from your part

You still haven't explained how it's in 19th Century textbooks if I "made it up"! 😂

If you don't remember Roman Numerals either, that's 1898

No wonder you can’t produce such a simple request.

says person who still hasn't produced a single textbook that supports anything that they say, and it's such a simple request 😂

That’s you saying it

No it isn't! 😂 Spot the difference 1/2(8)²=1/256 vs.

6(ab)2 does not equal 6a2b2

You are unambiguously saying a(b)^c somehow means (ab)^c=a^c b^c

Nope. Never said that either 🙄

except when you try to nuh-uh at anyone pointing out that’s what you said

Because that isn't what I said. See previous point 😂

Where the fuck did 256 come from if that’s not exactly what you’re doing?

From 2(8)², which isn't the same thing as 2(ab)² 🙄 The thing you want it to mean is 2(8²)

snipping about terms I am quoting from a textbook you posted,

Because you're on a completely different page and making False Equivalence arguments.

you wanna pretend 2(x-b)2 isn’t precisely what you insist you’re talking about?

No idea what you're talking about, again. 2(x-b)2 is most certainly different to 2(xb)2, no pretense needed. you're sure hung up on making these False Equivalence arguments.

Show me any book where the equations agree with you

Easy. You could've started with that and saved all this trouble. (you also would've found this if you'd bothered to read my thread that I linked to)...

Thus, x(x-1) is a single term which is entirely in the denominator, consistent with what is taught in the early chapters of the book, which I have posted screenshots of several times.

I’ve posted four examples to the contrary

You've posted 4 False Equivalence arguments 🙄 If you don't understand what that means, it means proving that ab=axb does not prove that 1/ab=1/axb. In the former there is multiplication only, in the latter there is Division, hence False Equivalence in trying to say what applies to Multiplication also applies to Division

all you’ve got is

Pointing out that you're making a False Equivalence argument. You're taking examples where the special Exponent rule of Brackets applies, and trying to say that applies to expressions with no Exponents. It doesn't. 🙄 The Distributive Law always applies. The special exponent rule with Brackets only applies in certain circumstances. I already said this several posts back, and you're pretending to not know it's a special case, and make a False Equivalence argument to an expression that doesn't even have any exponents in it 😂

Juxtaposition is key to the bullshit you made up

Terms/Products is mathematical fact, as is The Distributive Law. Maths textbooks never use the word "juxtaposition".

You made a hundred comments in this thread about how 2*(8)2 is different from 2(8)2

That's right. 1/2(8)²=1/256, 1/2x8²=32, same difference as 8/2(1+3)=1 but 8/2x(1+3)=16

Here is a Maths textbook saying, you’re fucking wrong

Nope! It doesn't say that 1/a(b+c)=1/ax(b+c). You're making a false equivalence argument

Here’s another:

Question about solving an equation and not about solving an expression. False equivalence again.

You have harassed a dozen people specifically to insist that 6(ab)2 does not equal 6a2b2

Nope! I have never said that, which is why you're unable to quote me saying that. I said 6(a+b)² doesn't equal 6x(a+b)², same difference as 8/2(1+3)=1 but 8/2x(1+3)=16

You’ve sassed me specifically to say a variable can be zero, so 6(a+b) can be 6(a+0) can just be 6(a).

That's right

There is no out for you

Got no idea what you're talking about

This is what you’ve been saying

Yes

you’re just fucking wrong

No, you've come up with nothing other than False Equivalence arguments. You're taking an equation with exponents and no division, and trying to say the same rules apply to an expression with division and no exponents, even though we know that exponent rule is a special case anyway, even if there was an exponent in the expression, which there isn't. 🙄

about algebra, for children

For teenagers, who are taught The Distributive Law in Year 7

Then why doesn’t the juxtaposition of mc precede the square?

For starters stop calling it "juxtaposition" - it's a Product/Term. Second, as I already told you, c²=cc, so I don't know why you're still going on about it. I have no idea what your point is.

In your chosen book

You know I've quoted dozens of books, right?

you can’t say shit about it

Again I have no idea what you're talking about.

expands 6(ab)3 to 6(ab)(ab)(ab)

Ah, ok, NOW I see where you're getting confused. 6ab²=6abb, but 6(ab)²=6abab. Now spot the difference between 6ab and 6(a+b). Spoiler alert - the latter is a Factorised Term, where separate Terms have been Factorised into 1 term, the former isn't. 2 different scenario's, 2 different rules relating to Brackets, the former being a special case to differentiate between 6ab² and 6a²b²=6(ab)²

P.S.

is like arguing 1+2 is different from 2+1 because 8/1+2 is different from 8/2+1

this is correct - 2+1 is different from 1+2, but (1+2) is identically equal to (2+1) (notice how Brackets affect how it's evaluated? 😂) - but I had no idea what you meant by "throwing other numbers on there", so, again, I have no idea what your point is

But you understand E=mc2 does not mean E=(mxc)2

I already answered, and I have no idea what your point is.

This is you acknowledging that distribution and juxtaposition are only multiplication

Nope. It's me acknowledging they are both BRACKETS 🙄

E=mcc=(mxcxc) <== BRACKETS

a(b+c)=(ab+ac) <== BRACKETS

and only precede

everything 😂

Please find a calculator that gives a result different to 128 for the expression 2(3+5)². Should be easy, no?

Please find a Maths textbook that backs that up as being the correct answer. i.e. Exponents before Brackets. Should be easy, no? 🤣

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 😂