 Hello and welcome to the session. In this session we discuss the following question which says carry out the following division 25ab into a cube minus b cube whole divided by 10 into a minus b. Before proceeding with the solution 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 in this question. Now let's move on to the solution. We need to divide 25ab into a cube minus b cube by 10 into a minus b. Firstly let's factorize each of the given expressions separately. First consider the expression 25ab into a cube minus b cube. Let us first factorize 25, 5, 5 times is 25 and 5, 1 times is 5 so we write 25 as 5 into 5. So this expression is equal to 5 into 5 into ab. Now we expand a cube minus b cube using the identity in the key idea. So this gives us a minus b into a square plus ab plus b square. In the same way we factorize the expression 10 into a minus b. Now 10 is factorized as 2, 5 times is 10 and 5, 1 times is 5. So 10 is written as 2 into 5 so this expression 10 into a minus b is equal to 2 into 5 into a minus b. Now 25ab into a cube minus b cube divided by 10 into a minus b is equal to, now the value of the expression 25ab into a cube minus b cube. That is this value 5 into 5 into ab into a minus b into a square plus ab plus b square upon the value of the expression 10 into a minus b. That is this value 2 into 5 into a minus b. Now here this 5 and this 5 gets cancelled a minus b and a minus b gets cancelled and we are left with 5 upon 2 into ab into a square plus ab plus b square. So our final answer is 5 upon 2 ab into a square plus ab plus b square. So this completes the session. Hope you have understood the solution for this question.