 Hello and welcome to another session on factorization So in this session we are going to learn how to factorize expressions of the form a plus b plus c times bc plus ca plus ab and minus abc. So this is the given expression and We are to factorize this. So how to go about it? So what we will do is? We will be first clubbing the b plus c together Okay, so here in the second bracket if you find out b plus c common from This one right so take a common from the last two Here you can take a common from here. So this this becomes bc plus a times b plus c correct minus abc next What we can do is we can now open the brackets accordingly. So hence if you see this is a bc So this goes to this right then a square b plus c then bc times b plus c then a Times b plus c whole square and then minus abc. This is the Expansion right so minus abc and plus abc will get struck off. So hence now if you see b plus c is common to all So b plus c is taken common and you get a square plus bc plus b plus c Sorry plus a times a b b plus c right Okay, so fair enough now you can again take Something common from here. Why because this is a square plus a b plus bc plus ac Okay, so I've just clubbed them in such a way that I can extract some common terms. So now this is a Common a plus b and here c common a plus b Correct, so hence a plus b can be taken as common one once again. So b plus c a plus b Times a plus c right or rearranging. You can see you can say a plus b plus b plus c Times c plus a is nothing but the given Expression right so this expression is reduced to this form, right? So whenever a plus b plus c into bc plus c a plus a b minus a b c is given then you can factorize it like that Okay, now Two corollaries can also be discussed here. So if you see we have now established this a plus b plus c times bc plus c a plus a b minus a b c is equal to a plus b b plus c c plus Correct now this can be rewritten as How can I write this as I can write this as a plus b plus c times b c plus c a plus a b minus a plus b b plus c C plus a is equal to a bc. This is let's say corollary number one Isn't it guys? So this is corollary number one and the other way we can write corollary number two can be written as a plus b plus c times b c plus c a plus a b is equal to a plus b b plus c c plus a plus a b c Correct. These are the two corollaries related to this particular Expression, okay, so now you know how to factorize these kind of expressions