Then you’re just a crank who lies to thirteen-year-olds about some bullshit you made up.
Weird then that’s in in Maths textbooks isn’t it 😂
Both 2(8+0)2 and 2(8*1)2
Says another person who can’t tell the difference between a(b+c) and a(bc) 🙄
Nobody but you has this problem
Knowing how to read Maths textbooks is a problem?? 😂 I can assure you that all my students have this same “problem”
Real math doesn’t work differently based on how you got there
It does if you have different expressions, such as 8/2(1+3) and 8/2x(1+3)
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
Different expressions, different order of evaluation, same rules of Maths (both following BEDMAS here) resulting in the different evaluations of the different expressions 🙄
Every textbook with an answer key says you’re full of shit.
Physical calculators say you’re full of shit.
Advanced math programs say you’re full of shit.
You can keep talking, but you’re obviously just full of shit.
At some point you’re either so deep in denial you should speak Swahili, or else being wrong on purpose is the point. The answer in either case is shut the fuck up.
2(n)2 is 2n2. Anything else is an inane complication nobody else believes in or uses or needs.
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 b * c - 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?
Then you’re just a crank who lies to thirteen-year-olds about some bullshit you made up.
Both 2(8+0)2 and 2(8*1)2 simplify to 2(8)2. They can’t get different answers.
Nobody but you has this problem. Real math doesn’t work differently based on how you got there.
Weird then that’s in in Maths textbooks isn’t it 😂
Says another person who can’t tell the difference between a(b+c) and a(bc) 🙄
Knowing how to read Maths textbooks is a problem?? 😂 I can assure you that all my students have this same “problem”
It does if you have different expressions, such as 8/2(1+3) and 8/2x(1+3)
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
Different expressions, different order of evaluation, same rules of Maths (both following BEDMAS here) resulting in the different evaluations of the different expressions 🙄
If you can simplify before distributing - and the PDFs you spam say you can - then there is no difference. You made it the fuck up.
2(n)2 is 2n2 whether n=a+b or n=a*b=ab. If you want to square the 2, that’s (2n)2.
It’s not about the multiply sign, or grouping, or division. You fooled yourself into saying 2=1.
They say you can do that when there is Addition or Subtraction inside the Brackets. They also say you cannot Distribute over Multiplication, at all
There is no difference between Addition and Multiplication?? 😂
And yet, there it is in textbooks that were written before I was even born 😂
Nope! a(b+c)=(ab+ac). a(bxc)=abc
…or 2²xn², or 2(½n+½n)²
Yes it is! 😂 If there’s a Multiply or a Divide, you cannot Distribute.
Not me! 😂
Every textbook with an answer key says you’re full of shit.
Physical calculators say you’re full of shit.
Advanced math programs say you’re full of shit.
You can keep talking, but you’re obviously just full of shit.
At some point you’re either so deep in denial you should speak Swahili, or else being wrong on purpose is the point. The answer in either case is shut the fuck up.
2(n)2 is 2n2. Anything else is an inane complication nobody else believes in or uses or needs.
Says person who can’t find a Maths textbook that says a(bxc)=(abxac) 🙄
I’m gonna presume that’s why you keep claiming a(bxc)=(abxac) 🙄
says person still not doing that 😂
No it isn’t! 😂 2xn² is
Except for authors of Maths textbooks 😂
So no answer for centuries of textbooks saying you’re full of shit.
b*c is one term.
Show me one textbook where a(b+c)2 gets an a2 term. Here’s four in a row that say you’re full of shit.
No it isn’t! 😂
says person who just proved they’re full of shit about what constitutes 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:
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 b * c - 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:
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?
b*c is the product of b and c.
Show me one textbook where a(b+c)2 gets an a2 term. Here’s four in a row that say you’re full of shit.