 Hello friends so welcome again to another session on factorization and in this session we are going to discuss another type of question where we are going to use grouping the terms to factorize. So let us say you have been given this particular question now on a you know first observation doesn't look like there is any common factors to be pulled out which we saw last session. So then we can try one thing is another thing to note here is the powers of A here is going down one by one isn't it? So it might give you indication that we have to group the term so if you see power of A goes from 3 to 2 then to 1 and then to 0 here right so that could be an indication. So what we can first do is let us first simplify it right and then we will club so I am writing it here club the variables together club the variables ok so here variables are x y and z. So let us try to club them together and let's see if we can extract out some common factors. So now before we you know start the solution please bear this thing in mind that you know there is no protocol or there no fixed root of factorization so you have to try out all the options which is there in your disposal and see whether any one of that can help you factorize it. So hence don't think that ok there would be step one, step two, step three. So you have to learn different types of factorization methods and then probably you know with experience when you solve multiple number of problems so you will get a feel or you will get a you know sense of factorization so hence don't lose heart if you are not able to solve it in the very first go. So let us try and solve this now. So what I said to you is you club the variables together so before that you just open up all the brackets so it is a square y minus ay minus az minus z please be very very careful careful with the signs because I have observed in my teaching experience that most of the students make mistakes not in finding the method right a method to factorize but some slight error here and there and then they end up losing that question itself. So hence please be very very careful while you are dealing with signs ok now so can I now club these two together yes x is the common variable and to our you know surprise we have we see a cube and a square so there are two is common as well so hence a square x is the common factor is it it. So a square x is common factor so what is left behind is nothing but a plus one right now in the second thing we can take minus ay common is it it ay is common so hence again you will see a plus one now we are getting some beautiful results here so if I get the same a plus one and third which we will indeed get if you take minus z then we have been able to find out one common factor and that is a plus one so let us take a plus one as common factor and then within brackets what is it a square x minus ay minus z is it. So this is the factorization we arrived at then this is clearly one factor we just need to check whether we can really go for factorization of the next term as well but it looks like you know it is very difficult to find out because z is an independent term over here there is no z anywhere same for x and y so we will have to stop here so we got the factorization like this this is the method by grouping the terms similarly let us give you another example let us say the question is x minus y whole square okay and minus five let us say minus five x minus y minus let us say x let us say five z let us keep it like five z x minus y and what else let us say there is I can say x minus y okay and this is because I am framing the question myself so let us say okay let me keep it like this so no z so let us say x minus y whole square and then minus five x minus y and then let us say minus z here minus z x minus y plus plus five let us say z okay so now let us see if we can really factorize this so again prime of AC looks like the power of 2 is decreasing here then same similar type of decrease of power here so can we club these two together so let us do that so if you see x minus y you take take common so what is left within is only but x minus y and then minus five isn't it and here also if you can take z common you will get x minus y minus five so again we got these two terms are common so hence I can write this as x minus y minus five times x minus y this term first here and then minus z this term comes here so now you see polynomial is reduced to its factors right how do I know it is factor because see there are two terms or two brackets and you know it's a multiplication of two expression right so so hence x minus y so in the last session we discuss this we can write this as x minus five x minus y minus five divides let us say this this entire thing was fx so instead of writing full thing I am writing x minus y minus five divides fx similarly x minus y minus z divides fx okay so I hope you understood the method