b*c is one term.
Show me one textbook where a(b+c)^2^ gets an a^2^ term. Here’s four in a row that say you’re full of shit.
Comment on I dunno
SmartmanApps@programming.dev 6 days agoEvery textbook with an answer key says you’re full of shit
Says person who can’t find a Maths textbook that says a(bxc)=(abxac) 🙄
being wrong on purpose is the point
I’m gonna presume that’s why you keep claiming a(bxc)=(abxac) 🙄
The answer in either case is shut the fuck up
says person still not doing that 😂
2(n)2 is 2n2
No it isn’t! 😂 2xn² is
Anything else is an inane complication nobody else believes in or uses or needs
Except for authors of Maths textbooks 😂
mindbleach@sh.itjust.works 6 days ago
SmartmanApps@programming.dev 6 days ago
b*c is one term
No it isn’t! 😂
say you’re full of shit.
says person who just proved they’re full of shit about what constitutes a Term 😂
FishFace@piefed.social 4 days ago
An algebraic expression written as a product or quotient of numerals or variables or both is called a term
So b * c, which is a product of the variables b and c, is a term, according to this textbook.
You seem to be getting confused because none of the examples on this particular page feature the multiplication symbol ×. But that is because on the previous page, the author writes:
When a product involves a variable it is customary to omit the symbol × of multiplication.
That means that the expression bc is just another way of writing b×c; it is treated the same other than requiring fewer strokes of the pen or presses on a keyboard, because this is just a *custom. That should clear up your confusion in interpreting this textbook (though really, the language is clear: you don’t dispute that b×c - or bc - are products, do you.)
Elsewhere in this thread you are clearly confused about what brackets mean. They are explained on page 20 of your textbook, where it says that you evaluate the expression inside the (innermost) brackets before doing anything else. Notice that, in its elucidation of several examples, involving addition and multiplication, the “distributive law” is not mentioned, because the distributive law has nothing to do with brackets and is not an operation.
Thus the expression 3 × (2 + 4) can be evaluated by first performing the summation inside the brackets to get 3 × 6 and then the product to get 18. The textbook then says that it is customary to omit the multiplication symbol and instead write 3(2+4), again indicating that these expressions are merely different ways of writing the same thing.
The exact same process of course must be followed whether numbers are represented by numerals or by letters designating a variable. You cannot do algebra if you don’t follow the same procedure in both cases. So consider the expression 2(a+b)². You have suggested that you must evaluate this as (2a+2b)² because you must “do brackets first”, but this is not what “doing brackets” means. You haven’t produced any authority to suggest that it is, and your own textbook makes it clear that “doing brackets” means do what is inside the brackets first. Not what is outside the brackets. Distributing 2 over a+b is not “doing brackets”; it is multiplication and comes afterwards.
If 2(a+b)² were equal to (2a+2b)² let us try with a=b=2. Let us first evaluate (2a+2b)²: it is equal to (2×2+2×2)² = (4+4)² = 8² = 64. Now let us evaluate 2(a+b)²: it is 2(2+2)² and now, following your textbook’s instruction to do what is inside the brackets first, this is equal to 2(4)². The next highest-priority operation is the exponent, giving us 2×16 (we now must write the × because it is an expression purely in numerals, with no brackets or variables) which is 32.
The fact that these two answers are different is because your understandings of what it means to “do brackets” and the distributive law are wrong.
Since I’m working off the textbook you gave, and I referred liberally to things in that textbook, I’m sure if you still disagree you will be able to back up your interpretations with reference to it.
By the way, I noticed this statement on page 23, regarding the order of operations:
However, mathematicians have agreed on a rule to fall back on if someone omits punctuation marks.
it does rather seem like this rule is one established not by the fundamental laws of mathematics but by agreement as they say, does it not? Care to comment?
SmartmanApps@programming.dev 2 days ago
So b * c, which is a product of the variables b and c
Nope. bc is the product of b and c. bxc is Multiplication of the 2 Terms b and c.
according to this textbook
Says person who clearly didn’t read more than 2 sentences out of it 🙄
none of the examples on this particular page feature the multiplication symbol ×
and why do you think that is? Do explain. We’re all waiting 😂 Spoiler alert: if you had read more than 2 sentences you would know why
That means that the expression bc is just another way of writing b×c;
No it doesn’t. it means bxc is Multiplication, and bc is the product 🙄 Again you would’ve already known this is you had read more than 2 sentences of the book.
it is treated the same other than requiring fewer strokes of the pen
No it isn’t, and again you would already know this if you had read more than 2 sentences. If a=2 and b=3, then…
1/ab=1/(2x3)=1/6
1/axb=1/2x3=3/2
this is just a custom
Nope, an actual rule of Maths. If you meant 1/axb, but wrote 1/ab, you’ve gonna get a different answer 🙄
That should clear up your confusion in interpreting this textbook
says person who only read 2 sentences out of it 🙄
though really, the language is clear:
It sure is when the read the rest of the page 🙄
you don’t dispute that b×c - or b * c - are products, do you
What don’t you understand about only ab is the product of a and b?
Elsewhere in this thread you are clearly confused about what brackets mean
Not me, must be you! 😂
They are explained on page 20 of your textbook, where it says that you evaluate the expression inside the (innermost) brackets before doing anything else.
Until all brackets have been removed. on the very next page. 🙄 See what happens when you read more than 2 sentences out of a textbook? Who would’ve thought you need to read more than 2 sentences! 😂
the “distributive law” is not mentioned, because the distributive law has nothing to do with brackets
And yet, right there on Page 21, they Distribute in the last step of removing Brackets, 🙄 5(17)=85, and throughout the whole rest of the book they write Products in that form, a(b) (or just ab as the case may be).
is not an operation
Brackets aren’t an operator, they are grouping symbols, and solving grouping symbols is done in the first 2 steps of order of operations, then we solve the operators.
Thus the expression 3 × (2 + 4) can be evaluated by first performing the summation inside the brackets to get 3 × 6 and then the product to get 1
3x6 isn’t a Product, it’s a Multiplication, done in the Multiplication step of order of operations.
The textbook then says that it is customary to omit the multiplication symbol and instead write 3(2+4)
It says you omit the multiplication sign if it’s a Product, and 3x6 is not a Product. I’m not sure how many times you need to be told that 🙄
again indicating that these expressions are merely different ways of writing the same thing
Nope, completely different giving different answers
1/3x(2+4)=1/3x6=6/3=2
1/3(2+4)=1/3(6)=1/18
You have suggested that you must evaluate this as (2a+2b)² because you must “do brackets first”
Yep
this is not what “doing brackets” means.
Yes it is! 😂
Not what is outside the brackets.
Yes it is! 😂 Until all Brackets have been removed, which they can’t be if you haven’t Distributed yet. Again, last step of the working out…
Distributing 2 over a+b is not “doing brackets”;
Yes it is! 😂 Until all Brackets have been removed
it is multiplication and comes afterwards
Nope, it’s Distribution, done in the Brackets step, before doing anything else, as per Page 21
following your textbook’s instruction to do what is inside the brackets first, this is equal to 2(4)²
Which, when you finish doing the brackets, is 8²
The next highest-priority operation is the exponent
After you have finished the Brackets 🙄
giving us 2×16
Nope. Giving us 8²=64
we now must write the × because it is an expression purely in numerals
Nope! If you write it at all, which you don’t actually need to (the textbook never does), then you write (2x4)², per The Distributive Law, where you cannot remove the brackets if you haven’t Distributed yet. There’s no such rule as the one you just made up
The fact that these two answers are different is because
You disobeyed The Distributive Law in the second case, and the fact that you got a different answer should’ve been a clue to you that you did it wrong 🙄
what it means to “do brackets” and the distributive law are wrong
No, that would be your understanding is wrong, the person who only read 2 sentences 🙄 I’m not sure what you think the rest of the chapter is about.
Since I’m working off the textbook you gave
Says person who only read 2 sentences out of it 🙄
I referred liberally to things in that textbook
Yep, ignoring all the parts that prove you are wrong 🙄
I’m sure if you still disagree you will be able to back up your interpretations with reference to it
Exact same reference! 😂
it does rather seem like this rule is one established not by the fundamental laws of mathematics but by agreement as they say
You know Mathematicians tend to agree when something has been proven, right? 😂
Care to comment?
Yep, read the whole chapter 🙄
mindbleach@sh.itjust.works 3 days ago
your own textbook makes it clear that “doing brackets” means do what is inside the brackets first. Not what is outside the brackets.
Which this troll admits when sneering “They say you can [simplify first] when there is Addition or Subtraction inside the Brackets.”
Except when they sneer you must not do that, because there’s addition inside the brackets. 2(3*a+2*a)^2^ becomes 2(5*a)^2^, which gets a different answer, somehow. Or maybe it’s 2(3a+2a)^2^ becoming 2(5a)^2^ that’s different. One or the other is the SpEcIaL eXcEpTiOn to a rule they made up.
Weird how nobody else in the world has this problem. Almost like a convention that requires special cases is fucking stupid, and if people meant (2(n))^2^, they’d just write that.
Distributing 2 over a+b is not “doing brackets”; it is multiplication and comes afterwards.
Which this troll literally underlines when sneering about textbooks they don’t read: “A number next to anything in brackets means the contents of the brackets should be multiplied.”
Except when they insist distribution is totally different from multiplication… somehow.
mindbleach@sh.itjust.works 6 days ago
b*c is the product of b and c.
Show me one textbook where a(b+c)^2^ gets an a^2^ term. Here’s four in a row that say you’re full of shit.
SmartmanApps@programming.dev 6 days ago
b*c is the product of b and c
Nope! bc is the product of b and c - it’s right there in the textbook! 😂
that say you’re full of shit.
Says person yet again who has proven they are full of shit about the definition of Terms 😂
mindbleach@sh.itjust.works 1 day ago
So no answer for centuries of textbooks saying you’re full of shit.