We can see the Acrobat window in those scans you found online.

...and the ones that came with the textbook, and not in the photo's 😂

You think 2(8)2 is 128 if that’s simplified from 2(8+0)2… but 256 if it’s simplified from 2(8*1)2. In short: no

says person who can't tell the difference between a(b+c) and a(bc) 😂

I think you’re about fifteen years old. You had an unpleasant teacher who belittled you, and you’ve identified with the aggressor. Your whole online persona is posturing to always be smarterer than everybody else

#EveryAccusationIsAConfession

Wolfram fucking Alpha is wrong about basic algebra

Which is an established fact

Faced with a contradiction that requires you to insist (8*1) ≠ (8+0)

again says person who can't tell the difference between a(b+c) and a(bc) 😂

The word you should be looking for is, “oops.”

yet again says person who can't tell the difference between a(b+c) and a(bc) 😂

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 🙄

There is no special case

So you're saying there no such rule as 2(ab)²=2a²b². Got it. you're admitting you're wrong then 😂

You made it up by confusing yourself about “dismissing a bracket.”

Says person who just claimed there's no such rule as the one they've been making the basis of their wrong claims 😂

To everyone else in the world, brackets are just another term

That's right. That's why you cannot separate the coefficient from it 😂

Several of the textbooks I’ve linked will freely juxtapose brackets and variables before or after

Several of your textbooks are outdated then

because it makes no difference

So is (2+3)-4 equal to -20 or 1? I'll wait

And that’s as factorization.

Wrong Factorisation. ab+ac=a(b+c)

This Maths textbook you plainly didn’t read was published this decade

And yet, is still wrong

Still waiting on any book ever that demonstrates your special bullshit

You were the one who just said there's no such special rule as 2(ab)²=2a²b² 😂

7bx with b=(m+n) becomes

7x(m+n)

and it’s the same damn thing

No, 7(m+n)x is invalid syntax due to ambiguity when x is negative.

Splitting it like 7xm+7xn is no different from splitting (m+n)/7 into m/7+n/7

That's right. I never said otherwise.

Brackets only happen first because they have to be reduced to a single term

They happen first because they already are a single Term...

A bracket with one number is not “unsolved”

Yes it is! If you haven't solved Brackets then you cannot progress onto Exponents.

it’s one number

Exactly! That's why you cannot separate the a from (b+c) - it's all ONE NUMBER 😂

Squaring a bracket with one number is squaring that number.

if it has been written as 2(ab)², not if it has been written a(b+c)². Also, again, there is no exponent in a(b+c), so that rule doesn't apply anyway 😂

Hence: 6(ab)3

6(ab)² <== note: not 6(a+b)², nor 6(a+b) for that matter. You're still desperately trying to make a False Equivalence argument 😂

It has a (b-c) term

No it doesn't. a(b-c) is one term

The base of an exponent is whatever’s in the symbols of inclusion.

And there's no exponent in a(b+c) 🙄

See page 121 of 696

See page 37

Also see page 282 and answers on page 577. x(x-1) is one term, as taught on page 37

In an expression such as 3a2,

3a² <== note: not 3(a+b), which has no exponent 🙄 It's hilarious how much effort you're putting into such an obvious False Equivalence argument 😂

You will never find a published example that makes an exception for distribution first

BWAHAHAHAHAHAHAH! I see you haven't read ANY of the sources I've posted so far then 🤣

refers to both 8x7 and 8(7) as “symbols of multiplication.”

Yep, present tense and past tense, since 8(7) is a Product, a number, as per Pages 36 and 37, which you're still conveniently ignoring, despite me having posted it multiple times

It’s just multiplication

Nope. 8(7) is a Product, a single Term, as per Pages 36 and 37. You won't find them writing 8(7)=8x7 anywhere in the whole book, always 8(7)=56, because it's a number

It’s not special, you crank

Yes it is, as per the textbook you're quoting from! 🤣

8(7) is a product identical to 8x7

Nope! 8(7) is a number, as per the textbook you are - selectively - quoting from 😂 8(7) is one term, 8x7 is two terms, as per Page 37

Squaring either factor only squares that factor

Where there are multiple pronumeral factors and you need the brackets to specify which factors the square is applying to, which, again, none of which applies to a(b+c) anyway Mr. False Equivalence 😂

Variables don’t work differently when you know what they are.

They're not variables if you know what they are - they are constants, literally a number as per pages 36 and 37

b=1 is not somehow an exception that isn’t allowed, remember?

That's right. a(1+c)=(a+ac), and you're point is??

There’s an exponent in 2(8)2

and no Pronumerals, and 2(8) is a number as per pages 36 and 37. 🙄And if you had read those pages, you would find it also tells you why you cannot write 2(8) as 28 (in case it's not obvious). if you want 2x8², then you can just write 2x8² 🙄

it concisely demonstrates to anyone who passed high school that you can’t do algebra

says someone who is trying to say that a rule about exponents applies to expressions without exponents 🤣