 Hi and welcome to the session. I'm Asha and I'm going to help you with the following problem which says factorize 27x cube plus y cube plus 8 cube minus 9xyz. So first let us learn a simple identity which says a cube plus b cube plus c cube minus 3abc is equal to a plus b plus c into a square plus b square plus c square minus ab minus bc minus ca. So with the help of this identity you will factorize the given problem. So this is our key idea. Let us now start with the solution. So we have to factorize 27x cube plus y cube plus z cube minus 9xyz. Now 27x cube can be written as 3x whole cube and thus this can further be written as 3x whole cube plus y whole cube plus z whole cube minus 3 into 3x into y into z which is in the form of the left hand side of the identity where a is equal to 3x, b is equal to y and c is equal to z and thus applying this identity it can be further written as a plus b plus c that is 3x plus y plus z and in the next packet we have a square that is 3x whole square plus b square that is y square plus c square that is z square minus a into b so a is 3x and b is y minus b into c so b is y and c is z minus c into a. So c is z and a is 3x which is further equal to 3x plus y plus z and in the next packet 3x whole square is 9x square plus y square plus z square minus 3 into x into y is 3xy minus yz minus 3x z. Hence on factorizing we get 3x plus y plus z into 9x square plus y square plus z square minus 3xy minus yz minus 3x z. So this is a solution hope you enjoyed this session take care and have a good day.