Factor yes, hence the special rule about Brackets and Exponents that only applies in that context
like how (8)22 only squares the 2
It doesn’t do anything, being an invalid syntax to follow brackets immediately with a number. You can do ab, a(b), but not (a)b
not (6ab)(6ab)(6ab)
Yep, as opposed to 6(a+b), which is (6a+6b)
3(x+1)2 for x=-2 is 3, not 9
No it isn’t. See previous point. Do we have an a(b+c), yes we do. Do we have an a(bc)²? No we don’t.
2(x-b)2 has a 2b2 term
No, it has a a(b-c) term, squared
shut the fuck up
says someone still trying to make the special case of Exponents and Brackets apply to a Factorised Term when it doesn’t. 😂 I’ll take that as your admission of being wrong about a(b+c)=ax(b+c) then. Thanks for playing
For a=8, b=1, that’s 2*(81)(8*1).
Only if you had defined it as such to begin with, otherwise the Brackets Exponents rule doesn’t apply if you started out with 2(8)², which is different to 2(8²) and 2(ab)²
…and there’s still no exponent in a(b+c) anyway, Mr. False Equivalence
We can see the Acrobat window in those scans you found online.
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.
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, even if that means saying Wolfram fucking Alpha is wrong about basic algebra.
Faced with a contradiction that requires you to insist (8*1) ≠ (8+0), you’re going to type laughter and spam emojis as if that inspires any reaction besides pity. The word you should be looking for is, “oops.”
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
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.
There is no special case. You made it up. 8+0 equals 8 (or sorry, does it just mean 8?) so 2(8+0)2 is the same as 2(8)2. The latter is the next step in simplifying the former. You’ve admitted simplifying first is valid, when your nose was rubbed in your own found PDFs doing exactly that.
You don’t have an opinion. You make no claim, anymore. All you have left are derision and emojis. You’ve admitted 2(8*1)2 means 2(8)(8), and insist that’s different from 2(8)2 because… ibid. You cannot explain it even now.
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 😂
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
So you’re saying there no such rule as 2(ab)²=2a²b².
That would mean 2(8*1)2 is 128. You are the one saying it’s not 2a2b2, because you think it’s 22a2b2, and that 2(8*1)2 is 256. I’m not touching anything without exponents because exponents are where you are blatantly full of shit.
if it has been written as 2(ab)², not if it has been written a(b+c)²
Source: your ass. Every published example disagrees, and you just go, nuh-uh, that up-to-date Maths textbook must be wrong. You alone are correct on this accursed Earth.
Page 129 of that PDF, exercise 5, question 14: simplify 2(e4)2. The answer on PDF page 414 is 2e8. Your bullshit would say 4e8.
Right below that, exercise 5*, question 4: 4(44)4. The answer on PDF page 414 is 1.72x1010. The bullshit you’ve made up would be 1.10x1011. 5* questions 7, 9, 10, and 11 also have the same a(b)c format as 2(8)2, if you somehow need further proof of how this actually works.
PDF page 134, exam practice question 10a, simplify 3(q2)2. PDF page 415 says 3q6. Your bullshit says 9q6.
Damn dude, that’s five textbooks you chose saying you’re full of shit, and zero backing you up. One more and I get a free hoagie. Your bullshit has brought us to max comment depth.
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. You made it up by confusing yourself about “dismissing a bracket.” To everyone else in the world, brackets are just another term. Several of the textbooks I’ve linked will freely juxtapose brackets and variables before or after, because it makes no difference.
Here’s yet another example, PDF page 27: (6+5)x+(-2+10)y. And that’s as factorization. This Maths textbook you plainly didn’t read was published this decade. Still waiting on any book ever that demonstrates your special bullshit.
7bx with b=(m+n) becomes 7(m+n)x and it’s the same damn thing. Splitting it like 7xm+7xn is no different from splitting (m+n)/7 into m/7+n/7. Brackets only happen first because they have to be reduced to a single term. A bracket with one number is not “unsolved” - it’s one number. Squaring a bracket with one number is squaring that number.
The base of an exponent is whatever’s in the symbols of inclusion. Hence: 6(ab)3 = 6(ab)(ab)(ab).
No, it has a a(b-c) term, squared
It has a (b-c) term, squared. The base of an exponent is whatever’s in the symbols of inclusion. See page 121 of 696, in the Modern Algebra: Structure And Method PDF you plainly got from Archive.org. “In an expression such as 3a2, the 2 is the exponent of the base a. In an expression such as (3a)2, the 2 is the exponent of the base 3a, because you enclosed the expression in a symbol of inclusion.” You will never find a published example that makes an exception for distribution first.
On the page before your screenshot - 116 of 696 - this specific Maths textbook refers to both 8x7 and 8(7) as “symbols of multiplication.” It’s just multiplication. It’s only ever multiplication. It’s not special, you crank. 8(7) is a product identical to 8x7. Squaring either factor only squares that factor.
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 🤣
That’s right
That’s right. It means 3abb=(3xaxbxb)
Factor yes, hence the special rule about Brackets and Exponents that only applies in that context
It doesn’t do anything, being an invalid syntax to follow brackets immediately with a number. You can do ab, a(b), but not (a)b
Yep, as opposed to 6(a+b), which is (6a+6b)
No it isn’t. See previous point. Do we have an a(b+c), yes we do. Do we have an a(bc)²? No we don’t.
No, it has a a(b-c) term, squared
says someone still trying to make the special case of Exponents and Brackets apply to a Factorised Term when it doesn’t. 😂 I’ll take that as your admission of being wrong about a(b+c)=ax(b+c) then. Thanks for playing
Only if you had defined it as such to begin with, otherwise the Brackets Exponents rule doesn’t apply if you started out with 2(8)², which is different to 2(8²) and 2(ab)²
…and there’s still no exponent in a(b+c) anyway, Mr. False Equivalence
We can see the Acrobat window in those scans you found online.
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.
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, even if that means saying Wolfram fucking Alpha is wrong about basic algebra.
Faced with a contradiction that requires you to insist (8*1) ≠ (8+0), you’re going to type laughter and spam emojis as if that inspires any reaction besides pity. The word you should be looking for is, “oops.”
…and the ones that came with the textbook, and not in the photo’s 😂
says person who can’t tell the difference between a(b+c) and a(bc) 😂
#EveryAccusationIsAConfession
Which is an established fact
again says person who can’t tell the difference between a(b+c) and a(bc) 😂
yet again says person who can’t tell the difference between a(b+c) and a(bc) 😂
PDFs found online. From which you are ignoring counterexamples using a(b+c)n. Fraud.
Your own spammed screenshots say 3 gets multiplied.
There is no special case. You made it up. 8+0 equals 8 (or sorry, does it just mean 8?) so 2(8+0)2 is the same as 2(8)2. The latter is the next step in simplifying the former. You’ve admitted simplifying first is valid, when your nose was rubbed in your own found PDFs doing exactly that.
You don’t have an opinion. You make no claim, anymore. All you have left are derision and emojis. You’ve admitted 2(8*1)2 means 2(8)(8), and insist that’s different from 2(8)2 because… ibid. You cannot explain it even now.
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 🙄
says the actual fraud who keeps ignoring that there is no exponent in a(b+c) 😂
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 😂
So you think 2(3x4x5)=(2x3x2x4x2x5) is totally fine? BWAHAHAHAHAHAHAAHA 😂😂😂
Weird then that it’s in Maths textbooks isn’t it, that 2(3x4x5) is in fact only equal to 2(60)? 😂
says person showing they don’t know the difference in meaning between “means” and “equals” 😂
Yep.
Yep.
Yep.
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.
That’s right, just facts, as per Maths textbooks 😂
a(b+c)=(ab+ac), same thing I’ve been saying the whole time
and facts
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.
No Multiplication. It’s not complicated 🙄
I already did. Not my fault you don’t understand the difference between Addition and Multiplication 😂
Your bullshit hit max comment depth.
So when you said 2(8)2 is 256, you were wrong.
Otherwise - walk me through how 2(8*1)2, 2(8+0)2, and 2(8)2 aren’t equal, alleged math teacher.
Tell me how a(b)n gets a different answer when you know the values. Gimme the primo bullshit.
“3(x+y) means 3*(x+y).”
“It depends on what the definition of is, is,” says someone definitely not trapped in a contradiction.
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.
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.
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)
who mysteriously owns dozens of Maths textbooks, many of which quoted in the post you’re avoiding 😂
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?
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?? 😂
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
That would mean 2(8*1)2 is 128. You are the one saying it’s not 2a2b2, because you think it’s 22a2b2, and that 2(8*1)2 is 256. I’m not touching anything without exponents because exponents are where you are blatantly full of shit.
Source: your ass. Every published example disagrees, and you just go, nuh-uh, that up-to-date Maths textbook must be wrong. You alone are correct on this accursed Earth.
Hey look, another one of the textbooks you insist I read says you’re completely wrong: “The multiplication sign is often not included between letters, e.g. 3ab means 3 * a * b.” Page 31 of the PDF… right above where you’ve dishonestly twisted the “expanding brackets” text. Next page: “3(x+y) means 3*(x+y).”
Page 129 of that PDF, exercise 5, question 14: simplify 2(e4)2. The answer on PDF page 414 is 2e8. Your bullshit would say 4e8.
Right below that, exercise 5*, question 4: 4(44)4. The answer on PDF page 414 is 1.72x1010. The bullshit you’ve made up would be 1.10x1011. 5* questions 7, 9, 10, and 11 also have the same a(b)c format as 2(8)2, if you somehow need further proof of how this actually works.
PDF page 134, exam practice question 10a, simplify 3(q2)2. PDF page 415 says 3q6. Your bullshit says 9q6.
Damn dude, that’s five textbooks you chose saying you’re full of shit, and zero backing you up. One more and I get a free hoagie. Your bullshit has brought us to max comment depth.
Firstly, it’s hilarious that you’ve gone back to a previous comment, thus ignoring the dozen textbook references I posted 😂
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 😂
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)
No I don’t. That’s why you can’t quote me ever saying that 🙄
and there are no exponents in a(b+c) and all this stuff about exponents is you being blatantly full of shit 🙄
No, this meme
Notice that there are no exponents? 😂
says person who came back to this post to avoid this post which is full of published examples that agree with me - weird that 😂
And I also pointed out why that was wrong here. i.e. the post that you have avoided replying to 😂
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).
Before the pages I already posted in the post that you are avoiding replying to 😂
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 😂
That’s right
Nope. Been telling you the whole time that is a special case, upon which you claimed there was no such special case 😂
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)
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. You made it up by confusing yourself about “dismissing a bracket.” To everyone else in the world, brackets are just another term. Several of the textbooks I’ve linked will freely juxtapose brackets and variables before or after, because it makes no difference.
Here’s yet another example, PDF page 27: (6+5)x+(-2+10)y. And that’s as factorization. This Maths textbook you plainly didn’t read was published this decade. Still waiting on any book ever that demonstrates your special bullshit.
7bx with b=(m+n) becomes 7(m+n)x and it’s the same damn thing. Splitting it like 7xm+7xn is no different from splitting (m+n)/7 into m/7+n/7. Brackets only happen first because they have to be reduced to a single term. A bracket with one number is not “unsolved” - it’s one number. Squaring a bracket with one number is squaring that number.
The base of an exponent is whatever’s in the symbols of inclusion. Hence: 6(ab)3 = 6(ab)(ab)(ab).
It has a (b-c) term, squared. The base of an exponent is whatever’s in the symbols of inclusion. See page 121 of 696, in the Modern Algebra: Structure And Method PDF you plainly got from Archive.org. “In an expression such as 3a2, the 2 is the exponent of the base a. In an expression such as (3a)2, the 2 is the exponent of the base 3a, because you enclosed the expression in a symbol of inclusion.” You will never find a published example that makes an exception for distribution first.
On the page before your screenshot - 116 of 696 - this specific Maths textbook refers to both 8x7 and 8(7) as “symbols of multiplication.” It’s just multiplication. It’s only ever multiplication. It’s not special, you crank. 8(7) is a product identical to 8x7. Squaring either factor only squares that factor.
Variables don’t work differently when you know what they are. b=1 is not somehow an exception that isn’t allowed, remember?
There’s an exponent in 2(8)2 and it concisely demonstrates to anyone who passed high school that you can’t do algebra.
So you’re saying there no such rule as 2(ab)²=2a²b². Got it. you’re admitting you’re wrong then 😂
Says person who just claimed there’s no such rule as the one they’ve been making the basis of their wrong claims 😂
That’s right. That’s why you cannot separate the coefficient from it 😂
Several of your textbooks are outdated then
So is (2+3)-4 equal to -20 or 1? I’ll wait
Wrong Factorisation. ab+ac=a(b+c)
And yet, is still wrong
You were the one who just said there’s no such special rule as 2(ab)²=2a²b² 😂
7x(m+n)
No, 7(m+n)x is invalid syntax due to ambiguity when x is negative.
That’s right. I never said otherwise.
They happen first because they already are a single Term…
Yes it is! If you haven’t solved Brackets then you cannot progress onto Exponents.
Exactly! That’s why you cannot separate the a from (b+c) - it’s all ONE 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 😂
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 😂
No it doesn’t. a(b-c) is one term
And there’s no exponent in a(b+c) 🙄
See page 37
Also see page 282 and answers on page 577. x(x-1) is one term, as taught on page 37
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 😂
BWAHAHAHAHAHAHAH! I see you haven’t read ANY of the sources I’ve posted so far then 🤣
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
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
Yes it is, as per the textbook you’re quoting from! 🤣
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
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 😂
They’re not variables if you know what they are - they are constants, literally a number as per pages 36 and 37
That’s right. a(1+c)=(a+ac), and you’re point is??
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 🙄
says someone who is trying to say that a rule about exponents applies to expressions without exponents 🤣