GCSE Maths - What is Difference of Two Squares (DOTS) #39

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  • Опубліковано 28 вер 2024
  • This video covers how to factorise expression into two brackets using the difference of two squares technique.
    This video is suitable for maths courses around the world.
    KS3 - Not on your course
    GCSE Foundation - All on your course
    GCSE Higher - All on your course
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КОМЕНТАРІ • 73

  • @Cognitoedu
    @Cognitoedu  3 роки тому +19

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  • @alecisfictional
    @alecisfictional 3 роки тому +108

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  • @zelplayz5165
    @zelplayz5165 2 роки тому +30

    I am very thankful for these videos, they are perfectly explained. My current revision is bcc Bitesize and it doesn’t make any sense. Thanks to you it all comes together. You earned another subscriber and be happy for helping so many people!

    • @Cognitoedu
      @Cognitoedu  2 роки тому +6

      Ah thank you very much Zel, we're glad we could help 😊

  • @yazanqazzaz4127
    @yazanqazzaz4127 3 роки тому +10

    you saved me from the math exam with this video and several others .
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    • @Cognitoedu
      @Cognitoedu  3 роки тому +4

      Awesome, glad the videos have been helping 👍

  • @harrydonna90677
    @harrydonna90677 4 роки тому +24

    thank you so much, I finally understand!!!! 😂🙏🏻

  • @xaviertami120
    @xaviertami120 3 роки тому +3

    Thank you ❤️

  • @yahiamohamed1675
    @yahiamohamed1675 Рік тому +4

    What if the numbers cant be squared?

    • @th3ogking292
      @th3ogking292 4 місяці тому

      Then u don't use this method

  • @muthukamiya7348
    @muthukamiya7348 3 роки тому +1

    thank you

  • @yixyaxo
    @yixyaxo 7 місяців тому

    i actually love you so much omg

  • @bentlycepe4714
    @bentlycepe4714 3 роки тому +1

    thanks

  • @sirplus15jha11
    @sirplus15jha11 3 місяці тому

    thank youuuuu

  • @eb2151
    @eb2151 2 роки тому +4

    What is the difference of two squares
    Why do we call it the difference of two squares
    Why in this video we are going to look at a special technique for factorising expressions
    What is video
    What is special technique
    What does factorising expressions mean
    What do we call the difference of two squares and why do we call it the difference of two squares or dots technique
    Why does it only work for a particular type of expression and what does this mean
    Why is it sometimes hard to notice
    What does notice
    How come it’s where we have one thing that is being squared take away another thing being squared
    What does squared mean
    What does take away mean
    What does - mean and the small two on top mean
    How come we can represent it as a squared minus b squared and why did you write a2 - b2
    What does represent mean
    Why in an exam they can take the form of any numbers or letters
    What does it mean when doing an exam they can take the form of any numbers or letters
    Why is it the expressions can look very very different Like x squared minus twenty five and why did you write x2-25 when you said that
    How come or forty nine minus p squared and how come you showed 49 - p2 when you said that
    What does factorise these expressions mean
    How come to factorise these expressions all we need to do is figure out the two things that are being squared
    What does figure out mean
    How do we find the two things that are being squared
    What is an example
    Why in our a squared and b squared example that would be a and b
    What does it mean to stick them into two sets of brackets and why did you show (a ) (b )
    How come one where we add them together and why did it show + when you said it
    What does add them together mean
    How come you said a plus b and what does this mean
    Why the other where we subtract and it showed a - b
    What does subtract mean
    And how come so a minus b
    Why is it always the second thing you subtract from the first
    What is the second thing and first thing
    How come this rule by itself might not make much sense
    What does rule mean
    How come we’re going to have a go at these two questions now
    What does make much sense mean
    What does factorise mean
    How comes in this first one we are trying to factorise x squared minus twenty five
    How come the first thing to do is to figure out what is it that is being squared to get each of these two terms
    What does figure out mean
    What does each of these two terms mean
    How come for x squared it is easy to spot it if an x being squared
    What does easy to spot mean
    How come we can write that below
    What does below mean
    How come another way to think about it is we’re just finding the square root of x squared
    What does square root of x mean
    Why is it x
    What is that thing on the number and x
    Why do we do the same thing for twenty five that is five
    Why did you write a line and /25 and 5 down
    Why do we write that below as well
    How come all we have to do is put them into two sets of brackets
    What does it mean to put them into two sets of brackets and why did you write (x 5) ( 5) when you said that
    Why one where we add them together
    What does add them together mean
    And why another where we subtract them
    Why did it show (x+5) when you said add and (x-5) when you said subtract
    How come next up we have forty nine minus p squared and it showed 49 - p2
    How come in this case we need to know that forty nine is just seven being squared
    What is that thing on 49 and why is there a line going to seven
    How come that p squared is just a p being squared
    Why do we put the 7 and the p into our brackets
    What is p and brackets
    Why seven plus p and seven minus p
    Why are we having a go at these slightly harder ones
    What does slightly mean
    Why is it a bit different to what we’ve done so far
    Why is it because the two terms contain numbers and letters
    What are terms
    What does contain mean
    What is that x and y and the small two on them
    How come the way we work it out is exactly the same
    What does work it out mean
    What does exactly mean
    Why is the first step to find the square root of each term
    What does the first step is to find the square root of each term mean
    Why is the square root of 16x squared is just 4x
    What that thing in the middle of 16x2 and 4x
    Why is the square root of sixteen four
    Why is the square root of x x squared
    Why does the same thing work for 9 y squared
    Why is it’s square root 3y
    Why is the root of 9 3 and what does this mean
    Why is the root of y squared y
    How come all that’s left is to put 4x and 3y into the two sets of brackets
    Why 4x plus 3y in the first
    Why 4x minus 3y in the second and what does this mean
    What does factorise mean and why do we need to factorise 36 minus 4x squared
    Why because the square root of 36 is 6 and because the square root of 4x squared is two x our brackets is 6 plus 2x
    And 6 minus 2x and why did you write (6+2x) and (6-2x)
    How come in this first one we are trying to do 9 x squared minus 64
    How come we can square root the 9 x squared to get 3x
    What does x mean
    Why square root of 64 to get 8
    How come we get the bracket 3x plus 8 and 3x minus 8
    Why is the square root of p squared p
    Why did you write that thing in middle and p at down
    Why is the square root of 25q squared is 5 q
    How come we get p plus 5q and p minus 5 q
    How come you want to show that this technique of factorising really works
    What does technique of factorising really works mean
    How come we can do by expanding the brackets back out and what does this mean
    How come by double checking that it is equal to p squared minus 25 q squared
    How come to expand the bracket we do p times p
    What does times mean
    How come it is p squared and you wrote p with small two on it
    How come we do p times minus 5q which is minus 5pq
    Why did you write that thing from 5p to q and said 5p times q is 5pq
    Why do we do 5q times negative 5q
    What does negative mean
    Why is it minus 25 q squared
    How come the important thing to notice is that the two people terms in the middle will cancel each other out and what does this mean
    Why because-5pq plus 5pq equal zero
    And why does it equal zero and what does this mean
    How come what we’re left with is p squared minus 25 two squared and how come you wrote p2 - 25q2 when you said that
    How come it’s actually the same thing as we were given in the question and what does this mean
    Why should this always happen with this technique
    What does technique mean
    Why is it if we expand our brackets back out two of the terms should cancel out and what does this mean

    • @shahdal-samarrai735
      @shahdal-samarrai735 2 роки тому

      why.

    • @eb2151
      @eb2151 2 роки тому +1

      @@shahdal-samarrai735 why did you say why

    • @joshuadawson703
      @joshuadawson703 2 роки тому +2

      Thanks for the essay, I agree with u entirely

    • @eb2151
      @eb2151 2 роки тому +1

      @@joshuadawson703 what does essay and agree and entirely mean

    • @ninjaking7256
      @ninjaking7256 Рік тому +1

      @@eb2151 troll

  • @muffintheduck3095
    @muffintheduck3095 Місяць тому

    Wait but what if one of the numbers that are being factorised isnt a perfect square? Do we devide them by 2? Because we had a test yesterday and it was 50a² - 121

    • @muffintheduck3095
      @muffintheduck3095 Місяць тому

      So would the answer be (25a+11) (25a-11) ? Thats what my classmate put as his answer and i just copied him loll

    • @ADHAY-CHAVANKE
      @ADHAY-CHAVANKE 22 години тому +2

      I don't think you will read this but we have to take common out of the two for example
      27x^2 - 48y^2
      Take common
      3(9x^2 - 16y^2)
      Solve the bracket by regular method
      3(3x-4y)(3x-4y)
      and put 3 at its place
      Hope you find it useful 👍

  • @billykasai9792
    @billykasai9792 2 роки тому +1

    Really a big help Thanks❤️🥂

  • @weevr4259
    @weevr4259 2 роки тому

    cheers mate

  • @zahraalredha2525
    @zahraalredha2525 3 роки тому +1

    what if the number cant be squared? ex 3x^2 - 108

    • @dekucuredmydepression5273
      @dekucuredmydepression5273 3 роки тому

      i think in THAT case,, you just have to use another rule or sumn

    • @djedg10
      @djedg10 2 роки тому

      For your example, sqrt(108)=6sqrt3.
      So we can factor out 3(x+6)(x-6)
      Another way to see it is to divide the expression by 3. Factorise x^2-36, then multiply the difference of two squares by 3 again to give 3(x+6)(x-6)

    • @Isabelle-nd7pj
      @Isabelle-nd7pj 7 місяців тому +1

      @@djedg102 years late lol but this was helpful, thank you!!

  • @joshuadawson703
    @joshuadawson703 2 роки тому +25

    You are my revision I just listen to you and it works, did my biology exam yesterday and I knew everything thanks to you

  • @AzaelMoshabe
    @AzaelMoshabe 4 місяці тому

    Thank you

  • @Yusra-d3w
    @Yusra-d3w 2 роки тому +14

    please never stop making these videos, they help a lot, you are my number 1 revision video source

  • @fezilendzinisa9236
    @fezilendzinisa9236 3 роки тому +18

    Very clearly explained. Thank you! ❤️

    • @Cognitoedu
      @Cognitoedu  3 роки тому +1

      Glad you enjoyed it Fezile!

  • @tr4shpanda281
    @tr4shpanda281 Рік тому +2

    thank you but what if the problem is a plus what will you do then?

  • @davidnathanielnaicker2351
    @davidnathanielnaicker2351 Рік тому +4

    Cheers mate,this guy right here absolute legend ,I'm in grade 10 but I'll be watching you till I'm in...well forever,very calming and relaxing and good easy methods,gotta love it

    • @davidnathanielnaicker2351
      @davidnathanielnaicker2351 Рік тому +2

      I actually ended up failing that paper but it's okay because I'm working hard to do well this term

    • @floofybons2775
      @floofybons2775 Рік тому +1

      Good luck 😅🎉

    • @enyplayz1514
      @enyplayz1514 11 місяців тому

      that's good mate, keep up the harde work😀@@davidnathanielnaicker2351

  • @jamalyusuf6377
    @jamalyusuf6377 2 роки тому +2

    you make math easier like nothing thanks very much

  • @quiinfuujojwaneh4696
    @quiinfuujojwaneh4696 Рік тому +2

    Thank you so much for this , now I understand ♥️

  • @larugon777
    @larugon777 4 місяці тому

    what if the numbers you need the square root of can be square rooted into while numbers?

  • @acet4831
    @acet4831 3 роки тому +2

    Your the best

  • @gehadmohamed1180
    @gehadmohamed1180 Рік тому +1

    I have a math exam tomorow and l was litterly crying before w
    Watching this 😊

  • @Bettymora7
    @Bettymora7 Місяць тому

    2:30 how did it became 7?

  • @shatindayrit5113
    @shatindayrit5113 19 днів тому

    bro tysm

  • @aliyanhashmi4188
    @aliyanhashmi4188 2 роки тому +1

    THANK YOU SO MUCH!!!

  • @silencer5854
    @silencer5854 5 місяців тому

    Ty

  • @Ultra-on-top
    @Ultra-on-top 10 місяців тому +1

    what if its -16+49x squared same method?

    • @n_nam_.
      @n_nam_. 9 місяців тому

      Sorry for the late response but I'm pretty sure it is

    • @Ultra-on-top
      @Ultra-on-top 9 місяців тому

      @@n_nam_. ty

  • @simpledimple984
    @simpledimple984 2 роки тому

    What should I do if I get an equation that can't be done like this? for example "12x^2-2"

  • @raghdelghemriny7262
    @raghdelghemriny7262 Рік тому

    I was dying not understanding the question

  • @nabeelkabbesh8724
    @nabeelkabbesh8724 2 роки тому

    Thx u made life way easier

  • @alieusesay6470
    @alieusesay6470 8 місяців тому

    Woow

  • @sheikhazraf3393
    @sheikhazraf3393 3 роки тому

    thank you so much!

  • @yusufakbar6186
    @yusufakbar6186 2 роки тому

    thank you

  • @magpiestudent9357
    @magpiestudent9357 2 роки тому

    Brilliant.

  • @khalidnashwan5021
    @khalidnashwan5021 2 роки тому +2

    This guy is a living legend i spent the last year trying to understand factorizing and i understood them here in a day thank u so much man

  • @danield9844
    @danield9844 2 роки тому

    what happens if one of the numbers weren't a square number

  • @thomas4839
    @thomas4839 3 роки тому +1

    Thank you so much, explained so clearly. Subscribed :D

  • @Letlotl0.M
    @Letlotl0.M 3 роки тому +1

    this video was really helpful

  • @hazelold2882
    @hazelold2882 3 роки тому

    Clearly explained

  • @perchefiore
    @perchefiore 2 роки тому +3

    Understood it easily, thank you so much!

    • @Cognitoedu
      @Cognitoedu  2 роки тому +1

      Great to hear, thank you!