 Hi and welcome to the session. I am Asha and I am going to help you solve the following question that says what are the possible expressions for the dimensions of the cuboids whose volumes are given below. So the volume of the first cuboid is 3x square minus 12x and the volume of the second cuboid is 12k by square plus 8k by minus 20k. So as we know the volume of a cuboid is equal to the length into breadth into height. So what we will try to do in this problem is to write this volume as the product of three factors such that one is length, another is breadth and other is height. So this is the key idea. We are going to use in this problem to determine the possible expressions for the dimensions of the cuboid. Let us now start with the solution and the first one is volume is equal to 3x square minus 12x. Now 3x is the common factor in both the terms so taking it common we are left with x minus 4. Now this is the product of three factors so one will be the length another will be the breadth and the last one will be the height. So the possible dimensions are and x minus 4. So this completes the first part and now proceeding on to the second part where volume of the cuboid is given as 12k by square plus 8k by minus 20k. 4k common from all the three terms we have 3y square left with the first term plus 2y with the second and minus 5 with the last. So we have 4k and thus by splitting the middle term we are written as 3y square plus 5 minus 3 into y minus 5 which is further equal to 4k into 3y square plus 5y minus 3y minus 5 is further equal to 4k. Now taking y common from the first two terms and minus one common from the last two terms we get y to 3y plus 5 minus 1 into 3y plus 5. Now taking 3y plus 5 common we have 4k into 3y plus 5 into y minus 1 and thus the volume is equal to 4k into 3y plus 5 into y minus 1. Hence our possible answer is 4k 3y plus 5 and y minus 1 since volume is equal to the length into breadth into height so any one of these can be the length, breadth and height. So our possible dimensions are 4k 3y and y minus 1. So this completes the solution. Hope you enjoyed this session. Take care and have a good day.