Expanding Using Pascal's Triangle
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- Опубликовано: 25 авг 2024
- Expanding binomials using Pascal's Triangle or Binomials Theorem can be very helpful when expanding it to a high power.
Once the pattern is learned and understood, even taking a binomials to a 10th power is no problem.
If you are watching this video, then you are probably making the best use of RUclips.
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 RUclips.
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
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
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 didn't know Pascal's triangle in my school. Now only, I learnt it, because of your help. Thank you very much.
Thanks for reminding me of Pascals triangle I leant 35yrs ago. You are awesome.
Glad you are back after 2 years sir!!
Please continue!! We love your work!!
I will try! 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
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!
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
Literally saved my life. So grateful for teachers that go out of their way to make these videos, thank you!
I'm a maths teacher and you're the best!
Thank for the awesome comment.
I appreciate it
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.
last-minute revision for my GCSE, thanks Mr H, you're a lifesaver
Glad it helped.
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!
thank you for the breakdown, didn't think i was going to get this.
No problem!
Way better than my teacher explained it. THANKYOU!
You're most welcome
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.
He's very straightforward in his explanations. Nice video.
Thisnis best and most concise explantiom inhave seen of this. Learned something today.
Brilliant Method! I'm going to use this technique as much as I can.
Fantastic!
excellent sir
i love your teaching
you are such a great teacher.. bless me sir
I'm italian and we call it "Triangle of Tartaglia" because Tartaglia was an important mathematician who found this before Pascal.
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.
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..
Awesomess. At school, they just made us memorize the formula. This is beautiful !
I am very excited about this teacher
Excellent! Mathematics is beautiful!😊
Wow !easy way! thank you for your time sir🙏
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!
I'm going to subscribed this channel because I actually learned something today. Thank you sir!
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 😀
This is now my favourite video from this channel.
I just love your simple method. Thanks
🙏
Excellent video, Sir!! All my respect
Never learnt this before. This is so coooool.
Absolutely beautiful. Thank you so much
You are excellent sri
Absolutely amazing property, thank you sir!!
Happy to see someone who appreciates math.
wonderful! THANK YOU!
Welcome!
You made me understand pascal's triangle thank you so much sir
Your a master sir thank you for teaching sir ❤🎉
It's my pleasure
Great overlay! And explanation :D
Tnx , ur video helped me a lot , keep making this videos so that maths can be a child's play
Didn't learn this school. Thanks a lot for this learning👍
Happy to help
Though I will admit my dream of a good set of notes came true. Having the online stuff now. Great reference.
Excellent teaching
Thanks for the comments! I appreciate them.
WOW why no body teach us like this ?????????? great man
I can only understand by your action and writing. Thank you sir 🙏🙏🙏
Helpful for me, now i can easily binomial theorem class 11
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 wish you the best in life, as well as your endeavors Mr. H
Thank you~
You saved my life ,finally.
simply brilliant
thanks man i am looking for this video
Thank you Sir🙏
Sir was finding it for a lot of time thanks for this upload
Most welcome
Amazing! Thanks a lot!
Thank you too!
If you want to learn more about this search binomial theorem
This is way more interesting and easy to remember.
Keep it up
You are a great teacher.
Agree
U just inspired me to open my own RUclips channel
Music to my ears!
thank you u saved me my final exam is tomorrow thhhhaaaanksssss
Good luck on your final!
I just thank you very much
well explained. Thanks
Brilliant
Wow! I enjoyed this 😘
excelente, well explained, than you
Thank you.
This is amazing!!
Incredible!!!!
Wonderful
Great Sirji
Genius! Why nobody taught me that? 😡😡😡
atleast I got to know about it in school yesterday and now here 😂😂😂
Do video for derivative(also functions) please, i need it as soon as possible, thank you
Now i can aso be one of the toppers😊
j'avais complètement oublié cette formule
🤣🤣ofc its this guy teaching math.
No hate this it helped me a lot😈💞💞
Thank you
than youu sir
Nice
Are you releasing a video on the binomial theorem?
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
THNKS MEHN
Holy moly thats a largo numero
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.
Sir, please start making jee relevant videos btw love your videos
Can you do subtraction with powers on both values
Nose bleeding again sir😂thank u again❤❤❤
So simple (3x+2y)^5=243x^5+162x⁴+108x³+72x²+48x+32.
it would be interesting to expand it without Pascal's triangle and with binomial theorem
Yes, I prefer the binomial theorem myself
so the green is the final answer?
Well that was easy. I'll try to remember that.
Glad you found it easy.
nice nice finally 😭😭
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.
Brillint
thanks sir i have an exam in 9 hours scary
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~
aka Yang's Triangle but then again it was Pascal who presented it to the world.
How do you make these videos?
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