The difference between a square and a number of cubs is positive. It implies the number is negative. m = - 3 whose square and cubs satisfy the condition.
By inspection m is - 3. Use synthetic division to get the other factor with (x+3) as one factor. Use the quadratic formula to get the other 2 roots. Simple, straight forward and easy. Thanks. 😢
@@SchoolClassMath And without the ugly echo in the audio, nor the long waste of our time talking to himself while he wrote it all out. I suggest you hire him to do your RUclips work for you.
@ stating the obvious? I could just plug numbers in like a trained monkey and that would eventually solve the problem. The truth is, a solution is BETTER when it is simpler and fast. Running through an algebraic humdrum like done here is a complete waste of time. And then the attitude that went along with that solution was wrong. STEM is not a club for which only some get to be a part. Everyone who likes to think gets to join. Choose a non-stem field if you can’t do this? That’s crap. This guy shouldn’t be in a STEM field.
@ what you say is correct, however it’s presented as a University entrance problem. It isn’t, it’s a very early problem on solving higher order equations. There is simply no need to intimidate people watching to learn by producing lengthy algebra solutions which aren’t necessary.
Once you find that m=-3 is one of the solutions, you can put the equation as (1): m^3-m^2+36=(m+3)(m^2+am+12)=0,a∈R ---(1) m^3-m^2+36=m^3+(a+3)m^2+(12+3a)m+36=0,a∈R -1=a+3,0=12+3a,a∈R a=-4 ---(2) (1)(2) m^3-m^2+36=(m+3)(m^2-4m+12)=0 This method is useful when you are having trouble factoring.
Call it the zero product rule. Some mathematics students don't know these terminologies that's why it's important to touch down on every detail while teaching this subject.
équation du 3eme degré donc 3 racines (solutions) dans cette équations 1racine réelle et 2 complexes je crois me souvenir qu'il existe des relations générales donnant les solutions pour l'équation du troisième degré et pas pour les degrés supérieurs
Exactly. It's not the answer that's the problem here, it's the question, good teachers don't set questions that can easily be guessed then spend 20 minutes doing it a 'long' way, it invites comments and attitudes like this. Why bother?
Everyone is not at the same level in Mathematics.......therefore we have to mention every basic rule, explain every dime, go to the root as much as u can, that is why
There is a much faster solution: You see that m must be -3 (because (-3)^2 - (-3)^3 = 9 - (-27) = 36)! Maybe there are other solutions as well because this is a cubic equation.
Yes, I agree with you sir. But there must be a general way of solving a problem, whatever the value of "m". What if the value of "m" is "0.85" ? That is, m^2 - m^3 = 1.34
@@SchoolClassMathIt's a variant of the Middle English surname Hereward, which combines the words here, meaning “army,” and weard, meaning “guard,” to form “army guard.” Today, the name is most commonly associated with the prestigious college, which was named after one of its founders, the English clergyman John Harvard.
Sometimes, we guess right when the answer is WHOLE NUMBER, what if the answer is decimal, fraction, irrational number etc. While guessing is brilliant, which is part of math.....it is also advisable to understand the actual process of solving a problem.
This was not a guess. It was analysis. 1: factorise both sides to see into the mathematical structure of the formulation 2: note that both sides then contain a repeated term. 3: test what happens if these two squares are presumed equal and discover the answer. It is not “guessing”. It is “insight” into the structure of the question. If you don’t like that, don’t set a question for which the answer is so easily found.
You say it is a Harvard Entrance Exam, but do I really need to write so much? Because I found all three roots just in 30 seconds in my head. Can I just write the answer?
Initial observations:: Although it's not specified, usually the variables m and n are used for integer, not general real numbers. Clearly m must be a negative number. Trying a few small values, it's clear that -3 works. Are there any other solutions? At this point I just watched the video.
So, you got -3 as a real root, what about the other two complex roots? I keep hearing these kind of comments again again on different videos. Someone is presenting a 6th degree polynomial with six roots and someone says they got the first two real roots by inspection. So, what! The Fundamental theorem of algebra says what ever the power of your leading coefficient, that’s how many possible roots you have, some possibly complex. So, you can’t just solve this in five seconds. It would be incomplete.
Instead of just using inspection to find -3 as a solution as some other commentors have suggested, consider the following: First of all, we look for an integer solution. Factoring the LHS we get m^2 (1-m) = 36 Consider now how 36 can be factored into a perfect square (m^2) and another integer (1-m): 36*1 or 9*4 or 4*9 or 1*36. So we have the 4 cases: (Case 1) m^2 = 36 and 1-m = 1 hence m = 6 or -6, while m=0 (a contradiction) (Case 2) m^2 = 9 and 1-m = 4 hence m = 3 or -3 while m=-3 ( m=-3 is a SOLUTION) (Case 3) m^2 = 4 and 1-m = 9 hence m = 2 or -2 while m=-8 (a contradiction) (Case 4) m^2 = 1 and 1-m = 36 hence m = 1 or -1 while m=-35 (a contradiction) Now with m=-3 as a solution, we know m+3 is a factor of the polynomial m^3-m^2+36 so by division we can get m^2-4m+12 as the other factor - then the Quadratic Formula will give us the other two (complex) solutions to our problem.
@@lee-mccoc7744 I don't doubt the correctness of yours maths but it is very long for such a simple problem which is solved as soon as you realise m must be negative the rest follows.
We are not on the same level.......a lot still need some basic explanation, nevertheless, we appreciate ur observation. it is already taken in over the subsequent videos. We love u all.
simply it can be told that no imaginary number while in square root we got imaginary number having negative sign. no need for carrying out such a long calculations afterwards
By inspection? What kind if an answer is that? So lazy. If the number on the left was not 36, say 35. Inspection will not work. Brobably logs at that point.
@@quakers200 if the answer was 35 the value of X would be between -3 and -2 and slightly greater than -3 so try - 2.9 etc in then -2.95 etc. This method is called iteration. Simple enough with a modern calculator.
Watch out for another question where the value of "m" is decimal fraction, then I will be so surprised if u can still manage to figure it out in 60 seconds.
@@SchoolClassMath It is the only way to get a positive with a square and a negative with cubic, when you do the numbers it adds. You can also have m square as a common factor multiplied in parenthesis by 1 - m. m has to be negative of value equal 3
I'm a retired Aeronautical Engineer ... 40 years ago, when I was 16, during my University entrance exams, the required level included derivatives ang integrals. Polinomical solutions of 3-degree ecuations wan learned at 13 years of age ...
@ No it doesn’t. You’re misleading people into thinking there’s a non-existent entry exam. Just put the problem up, don’t lie then say Harvard stands for a process. It doesn’t, you know it. Or if you don’t, I do.
You spend too much time on several trivial steps that are unnecessary. People who follow this type of video, know and understand these trivial steps. Walter Wen and Prolisine give more elegant solutions in their comments. Dr. Ajit Thakur (USA).
We are not on the same level.......a lot still need some basic explanation, nevertheless, we appreciate ur observation. it is already taken in over the subsequent videos. We love u al
The difference between a square and a number of cubs is positive. It implies the number is negative. m = - 3 whose square and cubs satisfy the condition.
Nice
By inspection m is - 3. Use synthetic division to get the other factor with (x+3) as one factor. Use the quadratic formula to get the other 2 roots. Simple, straight forward and easy. Thanks. 😢
Good observation
@@sivanaidoo5602, k
Ok
@@sivanaidoo5602 it’s easier than this.
@@SchoolClassMath
And without the ugly echo in the audio, nor the long waste of our time talking to himself while he wrote it all out.
I suggest you hire him to do your RUclips work for you.
I take my hat off to you my brother! This absolutely amazing! God bless you!
U are welcome
Hooray I am not going to a Woke School like Harvard.
@@GTKJNow Self opinion is also welcome
easy: factor left side
m²(1 − m) = 36
then, since 36 and m² are positive, 1 − m must be positive so m < 0, then m must be -3 since (-3)² (1 − -3) = 36
Many ways of solving math problem
@ stating the obvious? I could just plug numbers in like a trained monkey and that would eventually solve the problem. The truth is, a solution is BETTER when it is simpler and fast. Running through an algebraic humdrum like done here is a complete waste of time. And then the attitude that went along with that solution was wrong. STEM is not a club for which only some get to be a part. Everyone who likes to think gets to join. Choose a non-stem field if you can’t do this? That’s crap. This guy shouldn’t be in a STEM field.
@@oidbio2565 But you have two additional complex roots, which isn't so easy to find, if you don''t remember advanced algebra well.
An excellent explanation. Thank you!
Trivial problem. -3 by inspection. Then m^3-m^2+36=0. Divide lhs by x+3. Solve.
If it takes 20 min consider a non science degree.
Good observation
if you have to do it this way, consider a non-science degree. lol
You guys are too much😂😂😂 he was showing the entire picture of course they're faster ways to do it 😂😂😂
@well now that you have the answers in the various responses, you say that. Lol. I love how you guys love stating the obvious.
@ what you say is correct, however it’s presented as a University entrance problem. It isn’t, it’s a very early problem on solving higher order equations. There is simply no need to intimidate people watching to learn by producing lengthy algebra solutions which aren’t necessary.
Very well explained with no steps omitted and easy to follow every stage.
Thanks, really appreciated
An excellent explanation!
Thanks
Great thanks for a nice, clear explanation. Loved it.
I celebrate you, bro
Your explanation and solution are easy to follow. Excellent!
Thank you.
Thanks so much
simple and easy solution
one step only
Once you find that m=-3 is one of the solutions, you can put the equation as (1):
m^3-m^2+36=(m+3)(m^2+am+12)=0,a∈R ---(1)
m^3-m^2+36=m^3+(a+3)m^2+(12+3a)m+36=0,a∈R
-1=a+3,0=12+3a,a∈R
a=-4 ---(2)
(1)(2) m^3-m^2+36=(m+3)(m^2-4m+12)=0
This method is useful when you are having trouble factoring.
Good observation, that is the beauty of Mathematics. Thanks
Call it the zero product rule. Some mathematics students don't know these terminologies that's why it's important to touch down on every detail while teaching this subject.
Nice
In fact, this is systemically correct!!
Thanks
Nice information
u re wlc
Students will sleep if they listen to your explanation
People's learning rates are not the same
Absolutely you are right. I hope he is not a teacher, he is too boaring.
@@123prenyvkmg sometimes, a teacher needs to go in a steady pace to carry every student along....students assimilation is at different pace
@@123prenyvkmg BOARING !
True
m2-m3=36
m2(1-m)=9*4
m2=9 => m=-3 or m=3
1-m=4 => m=-3
m=-3
Good observation
équation du 3eme degré donc 3 racines (solutions) dans cette équations 1racine réelle et 2 complexes
je crois me souvenir qu'il existe des relations générales donnant les solutions pour l'équation du troisième degré et pas pour les degrés supérieurs
In my opinion it's faster using Horner method for polynomial. Why guessing a lot for 20 minutes?
Takes longer time to explain to slow learner
His yellow explanation section is a brilliant idea
Thanks
Exactly. It's not the answer that's the problem here, it's the question, good teachers don't set questions that can easily be guessed then spend 20 minutes doing it a 'long' way, it invites comments and attitudes like this. Why bother?
Everyone is not at the same level in Mathematics.......therefore we have to mention every basic rule, explain every dime, go to the root as much as u can, that is why
There is a much faster solution: You see that m must be -3 (because (-3)^2 - (-3)^3 = 9 - (-27) = 36)! Maybe there are other solutions as well because this is a cubic equation.
Yes, I agree with you sir. But there must be a general way of solving a problem, whatever the value of "m". What if the value of "m" is "0.85" ? That is, m^2 - m^3 = 1.34
Зачем разжевывать и растягивать на 20 минут? Люди могут сами самостоятельно быстро найти корни квадратного уравнения.
I love to contribute......but the language
Есть же переводчик. Я со своей стороны в будущем постараюсь ипользовать более простые фразы которые можно перевести однозначно.
How did you know that the operation in step 1 would be useful?
more explicit in other teaching video (Exponential Equation)
there is no such exam at harvard univ
The word HARVARD means something that is not just easy to scape through.....keep up guy
@@SchoolClassMathIt's a variant of the Middle English surname Hereward, which combines the words here, meaning “army,” and weard, meaning “guard,” to form “army guard.” Today, the name is most commonly associated with the prestigious college, which was named after one of its founders, the English clergyman John Harvard.
@@GTKJNow Good history
This is complication not soloution
This is the general way of solving problems like this....No matter how it's twisted.
From the initial inspection, it is clear that the unknown number m, is 3.
- 3 not 3
@@SchoolClassMath
Sorry about that. I just forgot to put the negative sign.
m^2(1-m) = 36
But we note 36 = (3^2)(4)
and thus m must be -3
Sometimes, we guess right when the answer is WHOLE NUMBER, what if the answer is decimal, fraction, irrational number etc. While guessing is brilliant, which is part of math.....it is also advisable to understand the actual process of solving a problem.
This was not a guess. It was analysis.
1: factorise both sides to see into the mathematical structure of the formulation
2: note that both sides then contain a repeated term.
3: test what happens if these two squares are presumed equal and discover the answer.
It is not “guessing”. It is “insight” into the structure of the question.
If you don’t like that, don’t set a question for which the answer is so easily found.
Good observation
You say it is a Harvard Entrance Exam, but do I really need to write so much? Because I found all three roots just in 30 seconds in my head. Can I just write the answer?
Yeah, you don't need to write so much but wait a moment, what are you going to do if probably the value of "m" is decimal fraction ?
Probably just click bait, he probably never graduated from Harvard. Looks like You need high GPA and or SAT to get in.
@@GTKJNow Free opinion
only m = -3. m =3 and m = 4 are extraneous
Observation
I use method parcial of derivates.
F(x) - m^3 = - 3m^2
m^2 - 3m^2 = - m^2
F'(x)- m^2 = - 2m
- 2m = 36
m = 36 / - 2
m = - 18
🤦♂️ if m = -18, m^2 - m^3 equals 6156
"m^2 - 3m^2 = - m^2"
And also, this is incorrect: 'm^2 - 3m^2 = - 2m^2".
lol
You probably have changed the question
m^2(1-m)=36
1-m=4(as 9×4=36)
m=-3
Ok
Initial observations:: Although it's not specified, usually the variables m and n are used for integer, not general real numbers. Clearly m must be a negative number. Trying a few small values, it's clear that -3 works. Are there any other solutions? At this point I just watched the video.
Appreciated
Holy crap! i just looked at it and in 15 seconds on quick substitution had it.
U mean ?
Surprised it took you 15 seconds!
So, you got -3 as a real root, what about the other two complex roots? I keep hearing these kind of comments again again on different videos. Someone is presenting a 6th degree polynomial with six roots and someone says they got the first two real roots by inspection. So, what! The Fundamental theorem of algebra says what ever the power of your leading coefficient, that’s how many possible roots you have, some possibly complex. So, you can’t just solve this in five seconds. It would be incomplete.
@@1234larry1 I'm glad you care, but I don't.
@@1234larry1This observation is one of the greatest.......really appreciated
After all that, you didn't even check that the complex solutions were also correct?
Good observation.... really appreciated
m^3 -m^2 + 0m + 36 = 0
m^3 -m^2 + 0m + 36 divided by m+3 is
[m^3 + 3m^2 - 4^m^2 - 12m + 12m + 36]/(m+3) = m^2 -4m +12
so m = -3 or m = [4+-sqrt(16-48)]/2 = 2+-isqrt(36)/2 = 2+-3i
U are welcome
( 10x10 ) - ( 4X4X4 ) = 36 100 - 64 = 36
With this, what will be the value of "m" ?
Harvard doesn't have an entrance exam.. they go by SAT scores
You lossed me when you got to M\2-M3 -36 = 0. why would the answer not be just 0 for all the left side or just some numbers that balance out?
Yeah, that is just another way of viewing it
Call it difference of two squares so that your students will understand.
Noted
Audio balance/tuning is definitely not one of yr majors.
That is a brilliant observation except it is not one of the best of the year
Instead of just using inspection to find -3 as a solution as some other commentors have suggested, consider the following:
First of all, we look for an integer solution.
Factoring the LHS we get m^2 (1-m) = 36
Consider now how 36 can be factored into a perfect square (m^2) and another integer (1-m):
36*1 or 9*4 or 4*9 or 1*36.
So we have the 4 cases:
(Case 1) m^2 = 36 and 1-m = 1 hence m = 6 or -6, while m=0 (a contradiction)
(Case 2) m^2 = 9 and 1-m = 4 hence m = 3 or -3 while m=-3 ( m=-3 is a SOLUTION)
(Case 3) m^2 = 4 and 1-m = 9 hence m = 2 or -2 while m=-8 (a contradiction)
(Case 4) m^2 = 1 and 1-m = 36 hence m = 1 or -1 while m=-35 (a contradiction)
Now with m=-3 as a solution, we know m+3 is a factor of the polynomial m^3-m^2+36 so by division we can get m^2-4m+12 as the other factor - then the Quadratic Formula will give us the other two (complex) solutions to our problem.
Good idea
m1=-3
m2=a-b
m3=a+b
m^3-m^2+36=0
m1+m2+m3= 1
-3+a-b+a+b= 1
2a=4
a=2
m1*m2*m3= -36
-3(a-b)(a+b)=-36
a^2-b^2=12
4-b^2=12
b^2=4-12=-8
b=2isqrt(2) or b=-2isqrt(2)
@@lee-mccoc7744 I don't doubt the correctness of yours maths but it is very long for such a simple problem which is solved as soon as you realise m must be negative the rest follows.
20 minutes?! Ridiculous
We are not on the same level.......a lot still need some basic explanation, nevertheless, we appreciate ur observation. it is already taken in over the subsequent videos. We love u all.
😮
Wow. I was working through, but need 2 sheets of paper.
Took me about ten seconds to recognize that m needed to be a negative number and then another 10 seconds to get to negative 3
What if m is a decimal, fraction, or irrational number ?
It always baffles me, how come any problem gets so easy after knowing the solution ?
Being at the simple end of the Dunning Krueger spectrum, that has always bothered me as well
That is the beauty of Mathematics...... bro
The answer is -3.
Exactly -3
Isn’t it just m=-3? Why waste so much pen and paper for something that’s staring you in the face?
Mathematics
@@SchoolClassMath You have to find the other two complex roots.
possibly in another video...Yeah
It is -3 - by just looking at it
What if the value of "m" is decimal, fraction or irrational number ? inspection method might not bail out
A third degree equation m^2 (m-1)= 36 which has no rintegr real solution
Observation
m = -3, 3, 4
(-3)^2-(-3)^3=36.
9-(-27)=36. Hence the answer is m=-3.
Good observation
10x10 = 100
4x4x4 = 64
100-64 = 36
@@mathewtom6478 Observation
@@mathewtom6478 Observation
I feel like 2x speed and muted would make this more clear
As speed is very much crucial, nevertheless understanding comes first
It is easy to guess -3.
Yeah, you are right, but what if the value of "m" is decimal fraction, any idea ?
Without any calculations I could see it was about a small value. First I tried with -2, then -3. And voilà!
It means you are a genius.... I welcome more ideas
m^2-m^3=36
=m^2-3=36
=1/m=36
1/m=36
m=1/36
Steps are so difficult to follow and not helpful for stidents
The Channel is about making solution simple as much as possible
Very helpful to me... especially the a+b =0. I never knew why one of them had to be zero. Education truly starts when you do it for fun, not exams
@@kiestbenny5482 That is great, that is the purpose of the channel
36=9+27
m²-9=m³+27
m-3=m²+9-3m
m²-4m+12=0
m=2±2√2i
or m=-3
m = -3
I'm surprised you have so few subscribers.
Everyone begins from somewhere, bro
Everyone begins from somewhere, bro
How many do not know the first step?
Naturally, people are in different levels
simply it can be told that no imaginary number while in square root we got imaginary number having negative sign. no need for carrying out such a long calculations afterwards
What if the "m" is a decimal fraction, irrational number?....suggestion might not be the way out
m should be equal to -3
m² -m³
(-3)² - (-3)³
= 9-(-27)
9+27=36
Therefore, m = -3
m³-m²+36=0 (m+3)(m²-4m+12)=0 m = -3
m²-4m+4+8=0 (m-2)²=-8 m = 2√2i+2 , -2√2i+2
On point
M^2-m^3 = 36 = 9 + 27
- or + ^2 always +
-^3 always -
As m^2 - m3 is impossible + with m +
So m must be - for 9 + 27 = 3^2 + 3^3
Then m = -3
Observation
I do not think this could be slowed down.
Yeah
It is obvious that the number had to be negative.
Good observation
√-1 doesnot a real number
By inspection? What kind if an answer is that? So lazy. If the number on the left was not 36, say 35. Inspection will not work. Brobably logs at that point.
I love this!
@@quakers200 if the answer was 35 the value of X would be between -3 and -2 and slightly greater than -3 so try - 2.9 etc in then -2.95 etc. This method is called iteration. Simple enough with a modern calculator.
@@quakers200 it is not maths I admit but it works. If you only had access to four figure tables it would require brains.
Many WILL know. So what is your point?
My point ? If the value of "m" is a decimal fraction, what is going to be done...suggesting or guessing ?
@ then why state that many will not know? Why the negarivity?
m^2(1-m)=36
(-3)^2(1+3)=36
m=-3
Really
Answer is M = -3. Took me less than 90 seconds using my brain.
Watch out for another question where the value of "m" is decimal fraction, then I will be so surprised if u can still manage to figure it out in 60 seconds.
My POV one by observation and other two by theory of polynomial
Nice one
m= -3 , m*m =9 , 1- m=4 4*9 =36
Yeah
m - 2x + N
Meaning that...
Nice
Thanks
m = -3, you can see it right away.
You are not wrong
Call it the sum of two cubes. You are teaching mathematics, let every detail count.
-3,solved in 0.00001 second in mind
You mean ?
@SchoolClassMath It was very easy for me
I pray we are all operating at the same higher frequency
Problems that seem boringly and insultingly obvious are still useful early practice for beginners though...
You might be right
-3 just read what it was posted on the video.
So your observation is ?
@@SchoolClassMath It is the only way to get a positive with a square and a negative with cubic, when you do the numbers it adds. You can also have m square as a common factor multiplied in parenthesis by 1 - m. m has to be negative of value equal 3
@@ggrape0 Good observation
m=-3.
Yeah, m = -3
Harvard University Entrance Exam? , so poor level really? ... I prefer to ask in a better University ...
Better university, such as ...?
I'm a retired Aeronautical Engineer ... 40 years ago, when I was 16, during my University entrance exams, the required level included derivatives ang integrals. Polinomical solutions of 3-degree ecuations wan learned at 13 years of age ...
-3...that took ten seconds of simple logic
Yeah, that is absolutely right, but what if m is fraction, decimal, irrational number ?
9+27= 36 hence x= -3
Yeah
M= -3
This is NOT an ``exponential question". You talk too much, sir. This is a 5 min. problem for competent student. It requires 3 lines.
We need to remember that, all students are not in the same level (of understanding)... need to carry every one along ..... sign of a good teacher
Ok
Thanks
9 + 27 = 36 = (-3)² - (-3)³
Of course yes
Bery slow.
Need to consider slow learners too
m= -3
Yeah. that is correct
There is no entrance exam to Harvard.
The word HARVARD stands for process that is not just easy to pass through, be it institutions, exams etc
@ No it doesn’t. You’re misleading people into thinking there’s a non-existent entry exam. Just put the problem up, don’t lie then say Harvard stands for a process. It doesn’t, you know it. Or if you don’t, I do.
@@kd8opi Harvard examination question
@ No it’s not. It’s just a math problem.
@@kd8opi Noted
Ya, like Fermat......
Meaning?
Thanks
You spend too much time on several trivial steps that are unnecessary. People who follow this type of video, know and understand these trivial steps. Walter Wen and Prolisine give more elegant solutions in their comments. Dr. Ajit Thakur (USA).
We are not on the same level.......a lot still need some basic explanation, nevertheless, we appreciate ur observation. it is already taken in over the subsequent videos. We love u al
Hoc m= ---3 est, respondeo. 😅😊😂
respondeo ?
Una solución real sera x = - 3
x =-3
m=-3 or m=2(1+sqr(2)i) or m=2(1-sqr(2)i)
You mean ?
m^3 - m^2 +/- m +36 = 0 , (m+3)(m^2-4m+12)=0 , m= -3 , m^2-4m+12=0 , m=(4+/-V(16-48))/2 , m=(4+/-V(-32))/2 ,
1 3 m=(4+/-i*V(32))/2 , m=2+/-i*V8 ,
-4 -12 solu , m= -3 , 2+i*V8 , 2-i*V8 , test , (-3)^2-(-3)^3=9-(-27) , 9+27=36 , OK ,
12 36 = 0 , test with WA , (2+i*V8)^2-(2+i*V8)^3=36 , (2-i*V8)^2-(2-i*V8)^3=36 , OK ,
Really appreciate this, it's actually making us getting better
@@SchoolClassMath Thanks , yes, let's inquire about the various solutions.
1001 definition
You mean ?
How to turn an exciting subject into absolute boredom.
You mean ?
@@SchoolClassMath The slow pace and repetition🤮🤮🤮🤮
Check other videos......you going to see that, this has been checked. Thanks, for the good observation
-3
It makes sense
5:18 I've lost the will to live ... Byeeee.
You mean ?
go faster
@mauriziodavoli8644, we really appreciate ur comments........this has been improved on. CHECK more videos
-6
-3