Not only did I learn a more efficient method of expanding, it also made me wonder what Pascal's triangle is and search for it. excellent channel and video
As soon as we started calculus in Engineering maths i had no idea what was going on because i was never taught pascal's triangle (which was the method the teacher was using). This really helped. Cheers mate.
Liked and subscribed! Thanks - an adult relearning math as a hobby who found your videos thanks to a recommendation from the YT algorithm on my home page.
oh my gosh, this s very easy when you started i didn't understand, but later i understood. thanks very much. God bless you for showing us your skills.we will subscribe and watch more.
I accidentally found your website recently. Your method of teaching math is phenomenal. I wished I had you as a math teacher when in High School. Thank you so much.
Fantastic! I didn’t do this on my maths curriculum back in the day but was a 1st maths student and still enjoy it! This was perfect to take my panicking 16 year old through this topic. It was also a great opportunity to teach her the absolute joys of a scientific calculator. Thank you!
You're just superb. It's the nonchalant manner in which you present your explanation that puts the icing on the cake Being a mathematical genius is an obvious quality of yours. And the simplicity is just superb. Cheers ..
The coefficients found from Pascal's Triangle perfectly match the coefficients found from a binomial-theorem expansion (whenever the exponent is a positive integer)
This guy has been helping me so much but i just got a question where theres only one letter thingy in the parentheses and the other is just a number (d+2)to the power of 8
You can put a letter in that number's place. For your example, let t = 2. Thus: (d + t)^8 = d^8 + 8*d^7*t + 28*d^6*t^2 + 56*d^5*t^3 + 70*d^4*t^4 + 56*d^3*t^5 + 28*d^2*t^6 + 8*d*t^7 + t^8 8th row of Pascal's triangle for reference: 1, 8, 28, 56, 70, 56, 28, 8, 1 Now evaluate each t-power at t=2, and have it join the coefficient. Put the d-power aside for later. 8*t = 16 28*t^2 = 28*4 = 112 56*t^3 = 56*8 = 448 70*t^4 = 70*16 = 1120 56*t^5 = 56*32 = 1792 28*t^6 = 28*64 = 1792 8*t^7 = 8*128 = 1024 t^8 = 256 Thus, the result is: d^8 + 16*d^7 + 112*d^6 + 448*d^5 + 1120*d^4 + 1792*d^3 + 1792*d^2 + 1024*d + 256
is there a faster way to do this by any method like factoring or something else? This was good to know but idk if its good to do it this way in an exam where we only have like an hour and a half to finish 100+ questions Thank you for the answer in advance sir!
Request on Convergence vs. Divergence please ? I have to go over it but it will be a bit before I get to it as I'm doing all of Calc I again. Though I 4.0 the class still. Currently 1/2 way through online. I never like being rushed in College. Math is like a fine wine and should be enjoyed ! Though not many would agree with me on that. 🤣
I take it you are talking about convergence and divergence, of an infinite series, as there are other meanings of those words. A sequence (or progression) is a list of numbers, a series is a summation of a sequence. Usually k represents the index of the individual term, and n represents the total number of terms. There is usually a function of k that determines the sequence value, although a sequence can also be recursively defined like the Fibonacci sequence. Some series add up to a finite value, when you have an infinite number of terms, which is called a series that converges, or convergent. Other series either add up to infinity, or continuously flip/flop between the same two numbers and never get closer to zero or to infinity, which is called a divergent series. Some series include an alternator term, of (-1)^k. If an alternating series only converges when it is alternating, it's called conditionally convergent, for instance the harmonic series of 1/k. If a series converges, regardless of whether it alternates, it's called absolutely convergent. The substance of Calculus's work with series, is to analytically determine whether or not it converges, and if so, what value it converges to. There are various tests for convergence, based on properties of the series definition, that may use limits, powers, roots, and integrals, to test which kind of convergence a series has.
Yes. You just let beta = -b. Expand (a + beta)^5, exactly as you would with this method. Assuming a is positive: Every odd exponent on beta, will materialize as a negative term when translated back to b. Every even exponent on beta, will materialize as a positive term when translated back to b.
Here's an example with a negative: Suppose it starts as (u - v)^3, where u and v are both positive numbers. Let w = -v. Now we've reduced it to (u + w)^3. Expand it out accordingly, with u's power descending from 3 to 0, and w's power ascending from 0 to 3. Coefficients follow 3rd row of Pascal's triangle, which is 1, 3, 3, 1. u^3 + 3*u^2*w + 3*u*w^2 + w^3 Since squared negatives are positive, this means all terms with w to an even power, will equal the same term with v replacing w. The opposite is true for cubed negatives. All terms with w to an odd power, will have a negative coefficient, and otherwise equal the same term. This gives us the result: u^3 - 3*u^2*v + 3*u*v^2 - v^3
If you are watching this video, then you are probably making the best use of UA-cam.
Yes!😅
Fully agree.
the hardest thing is to remember this when you don't use it regularly
Hehehe 🎉
"best use" academically speaking. This teacher is Awesome. But, There are other Great things here on UA-cam.
I recently found Mr H by chance and I've found his videos clear and easy to understand. Thank you, Mr H.
Thank you! 😊
if u found it easy then ur prolly dumb
Same Thank you very much I would fail math without your videos
Sir , iam 51 years old engineer and mathematician.You are one of the best teacher i saw in my life. Thank you very much
Wow, thanks. I appreciate your comment!
It's true
When your students who does not enjoy maths is inspired by your teaching you know you're a great teacher! Thank you so much!
i never actually learned pascal's triangle in school. thanks for teaching me!
Happy to help!
@@mrhtutoringsir I follow you but some things i don't understood
I didn’t learn it until college
I was hoping to see a cat...
Never knew this. Thank you for the topic
Thanks for reminding me of Pascals triangle I leant 35yrs ago. You are awesome.
I didn't know Pascal's triangle in my school. Now only, I learnt it, because of your help. Thank you very much.
Glad you are back after 2 years sir!!
Please continue!! We love your work!!
I will try! Thank you
Literally saved my life. So grateful for teachers that go out of their way to make these videos, thank you!
Not only did I learn a more efficient method of expanding, it also made me wonder what Pascal's triangle is and search for it. excellent channel and video
As soon as we started calculus in Engineering maths i had no idea what was going on because i was never taught pascal's triangle (which was the method the teacher was using). This really helped. Cheers mate.
Liked and subscribed! Thanks - an adult relearning math as a hobby who found your videos thanks to a recommendation from the YT algorithm on my home page.
Thanks for subscribing!
Way better than my teacher explained it. THANKYOU!
You're most welcome
Very nice reminder of Pascal's Triangle. Let me add: The Exponent of term to be expanded (call it 'n' ) results in 'n+1' Terms.
Thank you for the additional information
He's very straightforward in his explanations. Nice video.
oh my gosh, this s very easy when you started i didn't understand, but later i understood. thanks very much. God bless you for showing us your skills.we will subscribe and watch more.
Thisnis best and most concise explantiom inhave seen of this. Learned something today.
I accidentally found your website recently. Your method of teaching math is phenomenal. I wished I had you as a math teacher when in High School. Thank you so much.
Wow, thank you!
last-minute revision for my GCSE, thanks Mr H, you're a lifesaver
Glad it helped.
Fantastic! I didn’t do this on my maths curriculum back in the day but was a 1st maths student and still enjoy it! This was perfect to take my panicking 16 year old through this topic. It was also a great opportunity to teach her the absolute joys of a scientific calculator. Thank you!
Oh and if it helps
I did up to N12 for her to see the pattern. We laminated it along with theorem and applications!
the fact that an 8 minute video teaches me more than the 2hrs of lesson from my prof lol
Brilliant Method! I'm going to use this technique as much as I can.
Fantastic!
This is now my favourite video from this channel.
I'm a maths teacher and you're the best!
Thank for the awesome comment.
I appreciate it
I just love your simple method. Thanks
🙏
excellent sir
i love your teaching
you are such a great teacher.. bless me sir
Excellent! Mathematics is beautiful!😊
They say you can learn stuff from youtube, but would it be possible to do so, if we didn’t a teacher like Mr H ? My deepest gratitude to you sir.
Excellent video, Sir!! All my respect
Wow, I did'nt notice that the sum of the exponents led me to the exponent of the binomial, in this case five. Thanks professor!
You're very welcome!
You're just superb. It's the nonchalant manner in which you present your explanation that puts the icing on the cake
Being a mathematical genius is an obvious quality of yours. And the simplicity is just superb. Cheers ..
Thank you so much 😀
I'm going to subscribed this channel because I actually learned something today. Thank you sir!
Awesomess. At school, they just made us memorize the formula. This is beautiful !
thank you for the breakdown, didn't think i was going to get this.
No problem!
I am very excited about this teacher
This clears up so much that I didn’t know. Thanks you!
Absolutely amazing property, thank you sir!!
Happy to see someone who appreciates math.
Wow !easy way! thank you for your time sir🙏
Never learnt this before. This is so coooool.
I was never good enough at math to do math involving PT in high school, but I still enjoyed this video and understand the concept better now..
Absolutely beautiful. Thank you so much
Didn't learn this school. Thanks a lot for this learning👍
Happy to help
BRO I THESE 5 MINUTES YOU MADE ME UNDERSTAND THE WHOLE THING WHICH I THOUGHT I WILL FAIL TOMORROW IN TEST
Great overlay! And explanation :D
The coefficients found from Pascal's Triangle perfectly match the coefficients found from a binomial-theorem expansion (whenever the exponent is a positive integer)
I can only understand by your action and writing. Thank you sir 🙏🙏🙏
Your a master sir thank you for teaching sir ❤🎉
It's my pleasure
Tnx , ur video helped me a lot , keep making this videos so that maths can be a child's play
I have an exam today and part of it uses this, did not understand till now so thank you
I'm italian and we call it "Triangle of Tartaglia" because Tartaglia was an important mathematician who found this before Pascal.
You made me understand pascal's triangle thank you so much sir
Helpful for me, now i can easily binomial theorem class 11
Sir was finding it for a lot of time thanks for this upload
Most welcome
thank you u saved me my final exam is tomorrow thhhhaaaanksssss
Good luck on your final!
I just thank you very much
Excellent explanation. Thank you.
You are a great teacher.
Agree
WOW why no body teach us like this ?????????? great man
You saved my life ,finally.
I wish you the best in life, as well as your endeavors Mr. H
Thank you~
math equivalent of indian guy tech tips, life saver right here :D
Brilliant and to-the-point.
Though I will admit my dream of a good set of notes came true. Having the online stuff now. Great reference.
Thank you so much I needed this! 🙏
Thanks King, you made me a little less cooked.
wonderful! THANK YOU!
Welcome!
You are excellent sri
Excellent teaching
Thanks for the comments! I appreciate them.
simply brilliant
U just inspired me to open my own UA-cam channel
Music to my ears!
Wow! I enjoyed this 😘
If you want to learn more about this search binomial theorem
This is way more interesting and easy to remember.
Thank you Sir🙏
Are you releasing a video on the binomial theorem?
Amazing! Thanks a lot!
Thank you too!
thanks man i am looking for this video
Now i can aso be one of the toppers😊
🤣🤣ofc its this guy teaching math.
No hate this it helped me a lot😈💞💞
Genius! Why nobody taught me that? 😡😡😡
atleast I got to know about it in school yesterday and now here 😂😂😂
Great Sirji
Do video for derivative(also functions) please, i need it as soon as possible, thank you
Keep it up
well explained. Thanks
Can you do subtraction with powers on both values
Sir, please start making jee relevant videos btw love your videos
This is amazing!!
This guy has been helping me so much but i just got a question where theres only one letter thingy in the parentheses and the other is just a number (d+2)to the power of 8
You can put a letter in that number's place. For your example, let t = 2. Thus:
(d + t)^8 =
d^8 + 8*d^7*t + 28*d^6*t^2 + 56*d^5*t^3 + 70*d^4*t^4 + 56*d^3*t^5 + 28*d^2*t^6 + 8*d*t^7 + t^8
8th row of Pascal's triangle for reference:
1, 8, 28, 56, 70, 56, 28, 8, 1
Now evaluate each t-power at t=2, and have it join the coefficient. Put the d-power aside for later.
8*t = 16
28*t^2 = 28*4 = 112
56*t^3 = 56*8 = 448
70*t^4 = 70*16 = 1120
56*t^5 = 56*32 = 1792
28*t^6 = 28*64 = 1792
8*t^7 = 8*128 = 1024
t^8 = 256
Thus, the result is:
d^8 + 16*d^7 + 112*d^6 + 448*d^5 + 1120*d^4 + 1792*d^3 + 1792*d^2 + 1024*d + 256
is there a faster way to do this by any method like factoring or something else? This was good to know but idk if its good to do it this way in an exam where we only have like an hour and a half to finish 100+ questions
Thank you for the answer in advance sir!
Thank you.
excelente, well explained, than you
Request on Convergence vs. Divergence please ? I have to go over it but it will be a bit before I get to it as I'm doing all of Calc I again. Though I 4.0 the class still. Currently 1/2 way through online. I never like being rushed in College. Math is like a fine wine and should be enjoyed ! Though not many would agree with me on that. 🤣
I take it you are talking about convergence and divergence, of an infinite series, as there are other meanings of those words.
A sequence (or progression) is a list of numbers, a series is a summation of a sequence. Usually k represents the index of the individual term, and n represents the total number of terms. There is usually a function of k that determines the sequence value, although a sequence can also be recursively defined like the Fibonacci sequence.
Some series add up to a finite value, when you have an infinite number of terms, which is called a series that converges, or convergent. Other series either add up to infinity, or continuously flip/flop between the same two numbers and never get closer to zero or to infinity, which is called a divergent series. Some series include an alternator term, of (-1)^k. If an alternating series only converges when it is alternating, it's called conditionally convergent, for instance the harmonic series of 1/k. If a series converges, regardless of whether it alternates, it's called absolutely convergent.
The substance of Calculus's work with series, is to analytically determine whether or not it converges, and if so, what value it converges to. There are various tests for convergence, based on properties of the series definition, that may use limits, powers, roots, and integrals, to test which kind of convergence a series has.
If it is (a - b)^n do we use alternating addition and subtraction? E.g. a^3 - 3a^2b + 3ab^2 - b^3 for (a - b)^3
Yes~
Does with work with (a-b)^5 - or is there something similar?
Yes. You just let beta = -b.
Expand (a + beta)^5, exactly as you would with this method.
Assuming a is positive:
Every odd exponent on beta, will materialize as a negative term when translated back to b.
Every even exponent on beta, will materialize as a positive term when translated back to b.
j'avais complètement oublié cette formule
Incredible!!!!
How do you make these videos?
Brilliant
Nose bleeding again sir😂thank u again❤❤❤
it would be interesting to expand it without Pascal's triangle and with binomial theorem
Yes, I prefer the binomial theorem myself
Where is the binomial theorem video??
Well that was easy. I'll try to remember that.
Glad you found it easy.
What if negative
Here's an example with a negative:
Suppose it starts as (u - v)^3, where u and v are both positive numbers.
Let w = -v. Now we've reduced it to (u + w)^3. Expand it out accordingly, with u's power descending from 3 to 0, and w's power ascending from 0 to 3. Coefficients follow 3rd row of Pascal's triangle, which is 1, 3, 3, 1.
u^3 + 3*u^2*w + 3*u*w^2 + w^3
Since squared negatives are positive, this means all terms with w to an even power, will equal the same term with v replacing w.
The opposite is true for cubed negatives. All terms with w to an odd power, will have a negative coefficient, and otherwise equal the same term.
This gives us the result:
u^3 - 3*u^2*v + 3*u*v^2 - v^3