 Hi and welcome to the session, I am Asha and I am going to help you with the following question that says factorize each of the following and the second part is 64 n cubed minus 343 n cubed. So first let us learn that a cubed minus b cubed is equal to a minus b into a square plus a b plus b square. So this identity is our key idea that we are going to use in this problem to factorize it. Let us now begin with the solution and we have to factorize 64 n cubed minus 343 n cubed. Now we will write the given equation in the form of a cubed minus b cubed or 64 n by written as 4 cubed into n cubed minus 343 n by written as 7 cubed. Then we have n cubed or 4 m whole cube minus 7 n whole cube and on comparing this with the left hand side of this identity we find here that a is equal to 4 m and b is equal to 7 n. So in applying this identity this can further be written as a minus b that is 4 m minus 7 n into a square that is 4 m whole square plus a into b a is 4 m and b is 7 n plus b square that is 7 n whole square which can further be written as 4 m minus 7 n into 4 m whole square that is 16 m square plus 7 into 4 is 28 and we have m n plus 49 n square m minus 7 n into 16 m square plus 49 n square plus 28 m n. Thus on factorizing we get 4 m minus 7 n into 16 m square plus 49 n square plus 28 m n. So this completes the solution. Hope you enjoyed it. Take care and have a good day.