 Hey, hello friends welcome again to our session on factorization of algebraic expressions So we have been solving a lot of questions in this series and continuing that trend We are now trying to factorize this particular expression Okay, so the expression is 27 p cube minus 2 1 6 or 1 upon 2 1 6 minus 9 by 2 p square plus 1 by 4 p Now in the first look of it it looks like you know It's difficult to factorize it, but there are few indicators and those indicators are first There are four terms if you see what are indicators four terms are there and we learned that if four terms are there there could be possibility of a Binomial cube right and there is a cube term as well. So that is another supporting indicator cube terms Cube terms so you'll say no in binomial cube. You have two cube terms You it is appearing that it is only one here But if you look at two one six, that's also a cube at six cube actually So hence that makes me think that you know, I can use a cube of a binomial to factorize here So let's try and see whether it fits into our scheme So 27 p cube can clearly be written as 3 p cube. So first term is tentatively Achieve that okay 3 p whole cube. Now. What is minus 2 1 6 minus 2 1 6 is? 6 cube So the third term what should be the third term if you see if you remember a Minus b whole cube is what a cube minus 3 a square b Plus 3 a b square minus b cube So if you see we have got a cube and minus b cube see a cube and minus b cube So the other terms we have to just check with that in you know They are fitting into it or not and mostly it will be like that So can I you know so the square term is this one so and I have to take out a 3 so can I take out a 3? Yes, I can and then I have to write this as 3 p Because a has to be there then you have to square it Okay, because you need and then the other term should be 1 upon 6 and You see guys. This is actually 9 by 2 9 by 2 P square so it fits into my scheme then go for the next one here also you need a 3 So let's take out a 3 and then you need what? 3 p into 1 by 6 squared See whether it is 1 by 4 p actually it is 1 by 4 p. So hence this term This term matches with This term Correct and this term Matches with that term. So hence we are done. We got the expression. So hence. This is nothing but 3 p cubed Minus 3 times 3 p squared into 1 upon 6 plus 3 into 3 p times 1 upon 6 squared and Plus sorry not plus minus Minus What would that be that is 1 by 6 cube? Correct. So hence we got the expression like that and you know that this is nothing but cube of a binomial What binomial guys? This is 3 p minus 1 by 6 whole cube Which is now equal to 3 p minus 1 by 6 Into 3 p minus 1 by 6 into 3 p minus 1 upon 6 correct so What did we get as the final factorization? 3 p minus 1 upon 6 3 p minus 1 upon 6 and 3 p minus 1 upon 6 so check it you will get the same expression