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

[@Cognitoedu]

If you’d like to practise the material covered in this video, check out our platform at www.cognitoedu.org - it's totally free, and has been built to make learning and revision as easy as possible. The main features are: - Lessons organised by topic, only the lessons relevant to your specific exam board and tier are shown. - Automatic progress tracking. Progress bars tell you what you’re doing well at, and what you need to spend some time on. - Practise quizzes so you can test your knowledge. You can quiz yourself on any combination of topics you like. - A huge number of fully-hinted questions that take you step-by-step through some of the trickiest calculations & concepts. - A comprehensive bank of past exam papers, organised both by year, and also by topic. Amadeus & Tom

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[@Cognitoedu]

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

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[@yazanqazzaz4127]

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[@Cognitoedu]

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[@fezilendzinisa9236]

Very clearly explained. Thank you! ❤️

[@Cognitoedu]

Glad you enjoyed it Fezile!

[@khalidnashwan5021]

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

[@harrydonna90677]

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

[@jamalyusuf6377]

you make math easier like nothing thanks very much

[@Hayley-q4b]

THANK YOUUUU, I WAS STRUGGLING WITH THIS SM U EXPLAINED SO MUCH BETTER THAN CHAT GPT WHICH I ASKED TO HELP ME!! U RLLY SIMPLIFIED AND BROKE IT DOWN THANKSSS 😁

[@perchefiore]

Understood it easily, thank you so much!

[@Cognitoedu]

Great to hear, thank you!

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Thank you so much for this , now I understand ♥️

[@BrandonDuggan-o3t]

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[@xaviertami120]

Thank you ❤️

[@gehadmohamed1180]

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[@aliyanhashmi4188]

THANK YOU SO MUCH!!!

[@nabeelkabbesh8724]

Thx u made life way easier

[@tr4shpanda281]

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

[@NariPlaza]

Cannot be factorised

[@acet4831]

Your the best

[@larugon777]

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

[@simpledimple984]

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

[@yahiamohamed1675]

What if the numbers cant be squared?

[@th3ogking292]

Then u don't use this method

[@billykasai9792]

Really a big help Thanks❤️🥂

[@muthukamiya7348]

thank you

[@sirplus15jha11]

thank youuuuu

[@muffintheduck3095]

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]

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]

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 👍

[@aceindustries-o3b]

Please add a reply if you find it useful 😢

[@muffintheduck3095]

@@aceindustries-o3b thank you!! U made it so much easier to understand and im sorry for taking time out of your day to explain it. I really appreciate it🙏

[@CGEditz_0395]

@@muffintheduck3095it would not be 25a as you have to square root the 50 which is 7.071 and rounded that would be 7

[@weevr4259]

cheers mate

[@bentlycepe4714]

thanks

[@thomas4839]

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

[@Harley-i2s]

4:45 isn’t 25 squared, when square rooted, 25? It would surely need to be cubed to be 5, help

[@Harley-i2s]

Nvm they both give the same answer anyway so I’m assuming it’s just for the ease of smaller numbers

[@eb2151]

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]

why.

[@eb2151]

@@shahdal-samarrai735 why did you say why

[@joshuadawson703]

Thanks for the essay, I agree with u entirely

[@eb2151]

@@joshuadawson703 what does essay and agree and entirely mean

[@ninjaking7256]

@@eb2151 troll

[@Bettymora7]

2:30 how did it became 7?

[@_everlark_]

The square root of 49 is 7

[@Letlotl0.M]

this video was really helpful

[@magpiestudent9357]

Brilliant.

[@zahraalredha2525]

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

[@dekucuredmydepression5273]

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

[@djedg10]

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]

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

[@shatindayrit5113]

bro tysm

[@silencer5854]

Ty

[@hazelold2882]

Clearly explained

[@danield9844]

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

[@immenseangloid4168]

Just factorise normally E.g 3x² + 6x 3x(x+2)

[@raghdelghemriny7262]

I was dying not understanding the question

[@alieusesay6470]

Woow

[@yusufakbar6186]

thank you

[@AzaelMoshabe]

Thank you