 Hello and welcome to the session. In this session we are going to discuss the following question which says that find the product 1 2x square minus 3y whole square second part 3a plus 5b the whole into 3a minus 5b the whole and the third part is 5 plus 4x whole square we know that a plus b whole square is equal to a square plus 2ab plus b square similarly a minus b whole square is equal to a square minus of 2ab plus b square and a square minus b square can also be written as a plus b the whole into a minus b the whole with this key idea let us proceed to the solution now the first part of the question is 2x square minus of 3y whole square here we see that it will have the form a minus b whole square so here we can write a as 2x square and b as 3y and we know that a minus b whole square is equal to a square minus of 2ab plus b square so here we use this identity so we can write 2x square minus of 3y whole square is equal to a square that is 2x square whole square minus of 2 into a into b that is 2x square into 3y plus b square that is 3y whole square which is equal to 2 square that is 4 into x square whole square which is equal to x raise to the 4 minus of 2 into 2 that is 4 into 3 that is 12 into x square into y plus 3y whole square that is 9y square so we say that 2x square minus of 3y whole square is equal to 4 into x raise to the power 4 minus of 12 x square into y plus 9y square which is the required answer now we move on to the second part of the question that is 3a plus 5b the whole into 3a minus 5b the whole and here we see that we have to find the product of these two expressions that is the product of sum and difference of the same terms and here we use this identity that is a square minus b square is equal to a plus b the whole into a minus b the whole so we can write 3a plus 5b the whole into 3a minus 5b the whole as 3a whole square minus 5b whole square and this is equal to 3a whole square that is 9 into a square minus of 5b whole square that is 25 into b square so we can say that 3a plus 5b the whole into 3a minus 5b the whole is equal to 9a square minus of 25b square which is the required product now in the third part we have 5 plus 4x whole square it is the square of sum of two terms so here we can use this identity that is a plus b whole square is equal to a square plus 2ab plus b square here we can write a as 5 and b as 4x therefore we can write 5 plus 4x whole square as a square that is 5 square plus 2 into a into b that is 5 into 4x plus b square that is 4x whole square and this is equal to 5 square that is 25 plus 2 into 5 into 4 is 40 into x plus 4x whole square which is equal to 16x square we can rewrite this expression in descending parts of x as 16x square plus 30x plus 25 so 5 plus 4x whole square is equal to 16x square plus 40x plus 25 which is the required answer this completes our session hope you enjoyed this session