 Welcome guys once again to this session on problem solving and we are dealing with factorization I know factorization is a little tricky but trust me if you solve ample number of questions it will be very smooth and easy for you so hence have patience try as many problems as you can keep watching video solutions, video problem solving sessions and then take up standard textbook and start factorizing okay so the question here says there are these many terms six terms here and you have to factorize that means you have to convert or find out factors whose product will give you this expression correct now how to approach this so if you notice there are two types of variable one is x and y together like that and there is a b and then if you watch closely you there will be square terms these are the square terms and there are two ab terms as well is it twice the you know one variable times the other variable so this is suggesting that we can reduce it to a square is it similarly here also it can be reduced to a square how let us see so clearly x square plus two x y plus y square there is no brainer it is nothing but x plus y whole squared and on the other hand you can take minus one common and will be a square minus twice ab plus b square right I took minus out and hence the moment you took minus out of the brackets this will be reduced to this so what next clearly this will be nothing but x plus y whole square minus a minus b whole square so you must be very very thorough with the algebraic identities to solve such problems so the algebraic identities we are using here of a plus b whole square is equal to a square plus twice ab plus b square and another one is a minus b whole square is equal to a square minus twice ab plus b square isn't it and this is going to give us some advantage and if you see you are we are going to use this as well a square minus b square is equal to a minus b times a plus b y in this step if you see this is difference of two squares isn't it so I'm writing here please remember this this is nothing but difference of two squares and we know the moment there is difference of two squares we can be it can be factored very easily like that so my friends you can write this as x plus y minus a minus b so this is a minus b form and the other term will be x plus y plus a plus sorry not a plus a minus b isn't it so these are the two factors and hence if you see x plus y minus a plus b this is the factor number one factor number two would be x plus y plus a minus b okay so if you see we got x plus y a minus x plus y a minus b x plus y minus a plus b these are the two factors of this so what is the learning guys learning is observe observe if you can see difference of two squares then no big deal you can just use this relation and factorize it okay so learning is difference of two squares here