The Binomial Expansion

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  • Опубліковано 26 гру 2024

КОМЕНТАРІ • 81

  • @haseebkamran3051
    @haseebkamran3051 5 років тому +18

    I honestly cannot thank you enough. You have made this topic so easy for me. All of my teachers didn't teach me well enough but you did it perfectly! Thank you sm. God Bless

  • @enikanselurosemary7500
    @enikanselurosemary7500 4 роки тому +1

    Probably the best math teacher I've ever seen no cap

  • @ericokolalwambe2666
    @ericokolalwambe2666 Рік тому +1

    Thanks Sarah for these videos. Very useful. From Kenya🇰🇪

  • @--076
    @--076 4 роки тому +3

    You are an amazing teacher. Why couldn't any of my teachers teach this way.? Wow.

  • @StarfishMaths
    @StarfishMaths  9 років тому +13

    Thanks Abby, good spot! And yes I do plan on starting C2 very soon, thank you for your comments!

  • @NuraHm
    @NuraHm 6 років тому +13

    i wish you were my teacher ... amazing

  • @account1307
    @account1307 3 роки тому +1

    Thank you so much for making these videos, I have adhd and find it hard to revise by doing problems in a textbook, having someone go through calculations where I can pause the video and make sure im understanding properly is so so helpful!

  • @abbywalklett4855
    @abbywalklett4855 9 років тому +35

    At 9:52 doesn't 3x2x9x^2 = 54x^2 not 81x^2??

    • @abbywalklett4855
      @abbywalklett4855 9 років тому +2

      +Abby Walklett oh and will you be doing C2 and S1 because these videos are really good!

    • @frasierhuckle8453
      @frasierhuckle8453 9 років тому

      +Abby Walklett mmhmm

  • @asimiftikhar3867
    @asimiftikhar3867 6 років тому +36

    9:21 I guess you made an error. Its 54x^2 not 81x^2.

    • @aranshah5943
      @aranshah5943 4 роки тому +1

      Asim Iftikhar init

    • @helenday5031
      @helenday5031 4 роки тому +6

      Yes, there are one or two arithmetic errors, but still a great lesson wasn't it?!

    • @ace6285
      @ace6285 3 роки тому +5

      So glad you pointed that out. I am so insecure about my math ability that I was willing to believe her mistake.

  • @hussainzahidi4133
    @hussainzahidi4133 7 років тому +35

    at 9:24 . How did you get 81x^2 when you multiplied 3*2*9x^2 . I guess theres a miscalculation

    • @jeniven8630
      @jeniven8630 5 років тому +6

      yep..and i thought mine was incorrect xD

    • @rahoofamjad2365
      @rahoofamjad2365 5 років тому +6

      Yeah it is 54

    • @maramara2777
      @maramara2777 2 роки тому

      @@rahoofamjad2365 thanks lol i do have that same confusion

  • @rokithragavan1402
    @rokithragavan1402 4 роки тому +1

    goat teacher helped me for fm core pure 1

  • @Mwanatai
    @Mwanatai 3 роки тому

    You are real teacher
    GOD BLESS YOU FOR THAT CALLING

  • @gracepjs3281
    @gracepjs3281 4 роки тому +3

    This was so helpful, you explain it so well, keep up the good work 🙏🏾

  • @pien40bell
    @pien40bell 7 років тому

    I'd just like to say, no other video has got my brain to understand this part of C2, and trust me i've tried sooooo many videos and even my teachers... (who are useless, still havnt finished course and exam in less than 1 month). I thank you from the bottom of the heart.

    • @StarfishMaths
      @StarfishMaths  7 років тому +1

      Applea Salada Thank you for that - what a lovely comment! So pleased it helped. All the very best with your exams!

    • @maxhickman7376
      @maxhickman7376 7 років тому

      I literally couldn't agree and relate more

  • @linthasaleem6398
    @linthasaleem6398 7 років тому +5

    That was very well explained! Thankyou so much!

  • @account1307
    @account1307 3 роки тому

    Also I really appreciate your enthusiasm and positivity in these videos ^__^

  • @skullrazor
    @skullrazor 7 років тому +8

    Hey, isn't (3x2x9x^2) = 3*2*9 = 54*x^2 = "54x^2". You've gotten 81x^2 somehow.

  • @pazuzutru-truluv7094
    @pazuzutru-truluv7094 3 роки тому +1

    So many errors - 3 * 2 * 9x^2 = 54x^2 not 81x^2 - or am I missing something?

  • @dikshamatai7748
    @dikshamatai7748 6 років тому +3

    Make more videos 😭😭 your videos are soo good

  • @adewalefolarin1376
    @adewalefolarin1376 2 роки тому

    Woo! Amazing 😍,Good job...keep it up

  • @nadanahiyeh6977
    @nadanahiyeh6977 5 років тому +2

    It was helpful ! But like how did u get 81 when you multiplied 3x2x9 its (-54)

  • @Longgnose
    @Longgnose Рік тому

    9:12 I think there's a miscalculation there. 3X2X9X(x)^2 = 54x^2

  • @lot4cat
    @lot4cat 5 років тому

    so question, at 12:00 if the numbers weren't symmetrical would you use 5C3 or 5C2?

  • @irorunoluwa527
    @irorunoluwa527 2 роки тому +1

    I really appreciate it very much 😊

  • @mohammadjamil9915
    @mohammadjamil9915 5 років тому

    I honestly cant thank you enough , you just made that topic very easy for me so thank you ❤

  • @Antoniolive3k
    @Antoniolive3k 3 роки тому

    Amazing video.

  • @lot4cat
    @lot4cat 5 років тому +1

    i'm only 47 seconds into the video and my mind is already blown

  • @dmclll1381
    @dmclll1381 4 роки тому +1

    How did u get the answers for the C? In the question find the first 4 terms of (2-x)^6 in ascending order? Did u do it by pascal triangle or by the rule?

    • @ace6285
      @ace6285 3 роки тому

      My question as well. Still waiting for the answer.

  • @StarfishMaths
    @StarfishMaths  8 років тому +2

    Hi Giles, I'm not sure I understand your question completely. If you work out 5C3 either using the methods I went over, or on the calculator, you will get 10 and not 15! Does that help?

  • @Novokuv
    @Novokuv 8 років тому +6

    u r a cool person

  • @Mwanatai
    @Mwanatai Рік тому

    Be blessedreal richly Sara.
    I don't have enoughwords to Appreciate

  • @fridayyc
    @fridayyc 4 роки тому

    Thanks so much! That’s quite useful for me

  • @nimu4932
    @nimu4932 2 роки тому

    what would be done if they ask it in 'descending order' ?
    thanks :)

  • @Yahleetahmitchell
    @Yahleetahmitchell 4 роки тому

    God bless you! Thank you for this video

  • @trailershub993
    @trailershub993 4 роки тому

    great video

  • @MohammedHassan-nc8wp
    @MohammedHassan-nc8wp 3 роки тому

    Ma if equation change if this for instance (X-Y)4 or (X+5)5

  • @MemeOrbCo
    @MemeOrbCo Місяць тому

    9:33 -4 marks

  • @abdullahbsali
    @abdullahbsali 8 років тому +2

    Good video
    btw pascal didnt discover the triangle, other mathematicians studied it centuries before him in India, Persia (Iran) and China.

    • @I.OWN.NOTHING
      @I.OWN.NOTHING 5 років тому +2

      don't get salty

    • @user-aditi
      @user-aditi 4 роки тому

      @@I.OWN.NOTHING bruh we have every right to, shut up

  • @Gilesscoots
    @Gilesscoots 8 років тому

    At 12.01 howcome you get 10 and not 15 I understand you said it would be the same answer as they're symmetric but surely if you do 15 times instead of 10 it'll be bigger sorry if this is a bad question

  • @porkiie1999
    @porkiie1999 2 роки тому

    What if you have a negetive exponent

  • @aidenstonehouse9651
    @aidenstonehouse9651 5 років тому

    Very Nice!

  • @khaigailiaygai4510
    @khaigailiaygai4510 4 роки тому

    Before its difficult but its good now thank

  • @ziadnawfal955
    @ziadnawfal955 6 років тому

    Thanks... Really thanks ❤

  • @morebeans5874
    @morebeans5874 8 років тому

    thanks for this video it was a lot of help. will you be making more videos. plus can you make some for c2 and s1

  • @buddhabhandari4155
    @buddhabhandari4155 4 роки тому

    in last question why 1--6-15 are using to solve this probleem

    • @aranshah5943
      @aranshah5943 4 роки тому +1

      Buddha Bhandari that is my question

  • @feeneditz5102
    @feeneditz5102 6 років тому

    How do u do Independent term of x with pascal's triangle

    • @StarfishMaths
      @StarfishMaths  6 років тому

      Hi Whiplash, not entirely sure what you mean but try multiplying your coefficient form Pascal by the term you’re talking about. Hope that helps.

    • @feeneditz5102
      @feeneditz5102 6 років тому

      Find the term independent of x (the constant term) in the expansion of [x^2 -3/x] ^9

    • @StarfishMaths
      @StarfishMaths  6 років тому +1

      Hi Whiplash - that’s a good question - you’ll want to find the term where the positive power of x cancels out the negative one completely, leaving you with just a number. So it looks like that will be the term when x^2 is to the power of 3 (giving x^6) and (3x^-1) is to the power of 6. In this term then the binomial coefficients will also be 9C3 (or 9C6, both the same). Work out the whole term will all those 3 components to find your answer! Good luck!

    • @feeneditz5102
      @feeneditz5102 6 років тому +1

      ok i think i understand, any chance u could do a video on this it would help alot in my upcoming as math exam

  • @tshiamo.k
    @tshiamo.k 4 роки тому

    Merci✨

  • @awesomesauce8220
    @awesomesauce8220 2 роки тому

    👁️👄👁️ uhmm why didn't any of my teachers teach me this!!!! Like why make my life hard when they's a very simple way to do this ,, thank you so much 🙏👍, I literally have my A level last exams in the next two weeks , am def using this method...✨cheers✨🥂

  • @naveedahmed2653
    @naveedahmed2653 6 років тому

    Thanks

  • @Steve9Freestyle
    @Steve9Freestyle 9 років тому

    More maths! More maths! :D

  • @asktele3143
    @asktele3143 2 роки тому

    Example 2 it was 54x² not 81x²

  • @shotgunstrin4626
    @shotgunstrin4626 4 роки тому

    on a real one sarah would get it
    maths was good too

  • @DJGaming-ve8od
    @DJGaming-ve8od 7 років тому

    nice

  • @Mwanatai
    @Mwanatai 3 роки тому

    Shalom

  • @flawv3rm989
    @flawv3rm989 4 роки тому

    They r not powers of 11 lost 5 Mark's lol

  • @nuzaymadeeqsan6846
    @nuzaymadeeqsan6846 3 роки тому +1

    Please welcome to islam