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

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.
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[eb]

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

[larugon]

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

[trshpanda]

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

[simpledimple]

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

[thomas]

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

[muffintheduck]

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

[Ultra-on-top]

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