 Hey, welcome friends once again into this session of factorization of algebraic expressions and Here is one question given to us and the question is simplify x plus y whole cube minus x minus y whole cube Minus 6 y x square minus y square. So what should come to our mind the moment we see this question? One is the you know very usual method of using the identity is Opening the brackets are combining the like terms and get the simplified Expression that's one thing. What do I mean? So you have to you know open this term open this term open this term, right? opening means you just deploy the Identities what all identity so a plus b whole cube is what if you open this you will get a cube plus 3 a Square b plus 3 a b squared and plus b cube. This is one way of doing it Repeat the process for all the three terms this one this one and this one this one will be simply, you know Multiplication of the terms. That's it and then you club the like terms that is same power expressions together and then Find the simplified expression that is one way, but now that we have learned multiple other Identities it will be pertinent or let's say it will be very you know important to understand whether we can use those Identities as well and one is definitely there is the you know There are you can see two cubes are there and to you know two terms where x square y x y square kind of a setup is being Seen so can I write is like this? So this is x plus y Whole cube so whenever I see this one thing which comes in my mind is can I convert it into a Cube of a binomial expression or similar looking expressions, right? So and now let me open these brackets up. So or or what you can do is so what we can see here Here is that there is a cube term or cube term and there are certain terms which you know having multiple x and y together, right? so if I treat this as a cube and this as b cube and somehow get you know These terms 3 a square and 3 a b square term from this term Then I can reduce it to a cubic form. So how to go about it? So let's say if I treat a as x plus y and if I treat b as x minus y So in the given expression, I have I have got a cube and b cube very easily, right? No problem a cube is there b cube is there, but what about let's say, you know a square b plus a b square and 3 and 3 like that. So what about this? So if you see this term will be 3 a square if you want x plus y whole square times x minus y and this will be 3 x plus y and x minus y whole square Isn't it? This is what we have we have to get somehow So if you look at this expression, what is it? You can take three common x plus y common and x minus y common from it Both the terms have these three these this term common and with it within bracket what will be left out x plus y plus x minus y Am I right? Yes, and if the other way around that is if this was I had taken plus if I take minus then what will happen this will become this simply and And here I would have got minus Here I would have got minus so expression would be 3 x plus y x minus y and This term is nothing but 2 y see and then this becomes 6 y and x plus y and x minus y a minus b a plus b form x square minus y square and Surprisingly this matches my this expression here. Okay, so that's what I wanted to do So let's now solve it formally. I am writing it here so I can write this as x plus y whole cubed minus 3 So 6 y x square minus this thing 6 y x square minus y square can be written like This isn't it? This is same to 6 times y x square minus y square. So hence this is I can write 3 x plus y whole square x minus y then plus 3 x plus y and x minus y whole squared and minus x minus y whole cube Okay, so this 6 6 y x square minus y square Please remember can be written like that and since there was a minus sign So hence I had to change sign of so first it will be you know This minus and this will become plus because there was this minus sign over here I hope you got it if not then just you know just slow down the video pause the video look at the steps and Then again come back and resume it. Okay, so if this is satisfied then this looks like a This looks like a square B form This looks like a B square form and this looks like B cube form right So hence I can directly apply a cube a plus B or so this is minus so a minus B whole form whole cube so hence it will be x plus y and minus x minus y whole Cube and this expansion is given above Correct. So if you see what will this be so x and x will go so 2 y Cube so it becomes it becomes 8 y cube. So simplification is simply 8 y cube So, how does algebra is coming into picture? So Anyways, we are doing algebra, but then we use one particular methodology, which is algebraic identities. We used identities and we never Open the brackets up and try to simplify it. That was the learning. So hence the moment I saw two cubes and A term like this I started thinking that hey, it could be reduced into a Cube of a binomial form and then I don't need to do the Mechanical Multiplication part of it and hence I could simplify it to 8 y cube So if you open the brackets and solve it also, you will get the same thing 8 y cube