 Hello and welcome to the session. In this session we discuss the following question which says factorize 3x-2y whole cube plus 2y-5z whole cube plus 5z-3x whole cube. We know that if x plus y plus z is equal to 0, this implies that x cube plus y cube plus z cube is equal to 3xyz. This is the key idea to be used in this question. Now we move on to the solution. The given expression is 3x-2y whole cube plus 2y-5z whole cube plus 5z-3x whole cube. We take let 3x-2y be equal to a 2y-5z be equal to b and 5z-3x be equal to c. Then the expression 3x-2y whole cube plus 2y-5z whole cube plus 5z-3x whole cube is equal to a cube plus b cube plus c cube. Now consider a plus b plus c. This is equal to 3x-2y plus 2y-5z plus 5z-3x. Now this 3x cancels with minus 3x, 2y cancels with minus 2y, 5z cancels with minus 5z and this is equal to 0. That is we get a plus b plus c is equal to 0 and hence using the key idea this would mean that a cube plus b cube plus c cube is equal to 3abc. Now we substitute the values for a, b and c. We have a equal to 3x-2y. So 3x-2y whole cube plus b cube that is 2y-5z whole cube plus c cube that is 5z-3x whole cube. This is equal to 3abc that is 3 into 3x-2y into 2y-5z into 5z-3x. So this is our final answer. This completes the session. Hope you have understood the solution for this question.