 Hello and welcome to the session. In this session we discussed the following question which says factorize the following 18 aq bq minus 27 a square bq plus 36 aq b square and a x plus by whole square plus b x minus a y whole square. Before moving on to the solution let's recall the identity a plus b whole square is equal to a square plus 2ab plus b square and a minus b whole square is equal to a square minus 2ab plus b square. This is the key idea to be used in this question. Let's move on to the solution. The first expression given to us is 18 aq bq minus 27 a square bq plus 36 aq b square. From this expression we take out 9 a square b square common from all the three terms. So here we have 2ab minus 3b plus 4a. So the given expression is factorized as 9 a square b square into 2ab minus 3b plus 4a. Now the second expression given to us is ax plus by whole square plus bx minus a y whole square. Now we will open both these brackets using the identities given in the key idea. So for the first package we have ax plus by whole square. Now we will be using this identity a plus b whole square. So we get ax whole square plus 2ax into by plus by whole square plus now for the expression bx minus a y whole square we will use this identity that is a minus b whole square. So we have bx whole square minus 2 into bx into a y plus a y whole square. So this is further equal to a square x square plus 2abxy plus b square y square plus b square x square minus 2abxy plus a square y square. Now this further is equal to a square x square plus 2abxy plus b square y square plus b square x square minus 2abxy plus a square y square. Now 2abxy and minus 2abxy gets cancelled from the expressions a square x square and b square x square we take x square common and we left with a square plus b square. Now from these two expressions b square y square plus a square y square we take plus y square common and inside we have b square plus a square. Now we take a square plus b square common and then we are left with x square plus y square. So we give an expression ax plus b by whole square plus bx minus a y whole square is equal to a square plus b square into x square plus y square. So final answer is for the first expression we have 9a square b square into 2ab minus 3b plus 4a and for the second expression we have a square plus b square into x square plus y square. So this completes this session. Hope you have understood the solution for this question.