 Hello and welcome to the session. In this session we discuss the following question which says factorize 3x plus 2y whole cube minus 3x minus 2y whole cube. First let's recall the identity a cube minus b cube is equal to a minus b into a square plus ab plus b square. This is the key idea to be used for this question. Let's move on to the solution now. We need to factorize 3x plus 2y whole cube minus 3x minus 2y whole cube. Let us take 3x plus 2y as a and 3x minus 2y as b. So now we have 3x plus 2y whole cube minus 3x minus 2y whole cube equal to a cube minus b cube and using this identity we get this would be equal to a minus b into a square plus ab plus b square. Substituting the values for a and b we get 3x plus 2y whole cube minus 3x minus 2y whole cube is equal to 3x plus 2y minus 3x minus 2y into 3x plus 2y whole square plus 3x plus 2y into 3x minus 2y plus 3x minus 2y whole square. This is further equal to 3x plus 2y minus 3x plus 2y and this whole into 9x square plus 4y square plus 12xy plus 9x square plus xy minus 6xy minus 4y square plus 9x square plus 4y square minus 12xy. In this first bracket 3x minus 3x cancels when the second bracket 4y square minus 4y square cancels 12xy minus 12xy cancels 6xy minus 6xy cancels and now we are left with 2y plus 2y is 4y and this into 9x square plus 9x square plus 9x square is 27x square plus 4y square. So this expression 3x plus 2y whole cube minus 3x minus 2y whole cube is factorized as 4y into 27x square plus 4y square. So final answer is 4y into 27x square plus 4y square. So this completes this session. Hope you have understood the solution for this question.