 Hi and welcome to the session. I am Asha and I am going to help you solve the following problem which says if x plus y plus z is equal to 0 show that x cube plus y cube plus z cube is equal to 3 x y z. So first let us learn a simple identity which says x cube plus y cube plus z cube minus 3 x y z is equal to x plus y plus z into x square plus y square plus z square minus x y minus y z minus z x. So this identity is a key idea with the help of which we will show that x cube plus y cube plus z cube is equal to 3 x y z. So let us now start with the solution. Now as we are given that x plus y plus z is equal to 0. So on substituting x plus y plus z is equal to 0 on the right hand side of this identity we get x cube plus y cube plus z cube minus 3 x y z is equal to 0 into x square plus y square plus z square minus x y minus y z minus z x. And on multiplying 0 with any number the result is 0. So on the right hand side we have 0 and on the left hand side we have x cube plus y cube plus z cube minus 3 x y z which further implies that x cube plus y cube plus z cube is equal to 3 x y z. So thus we have proved that x cube plus y cube plus z cube is equal to 3 x y z. Hence proved. So this completes the solution. Hope you enjoyed it. Take care and have a good day.