 Hello and welcome to the session. In this session we discussed the following question which says Find the value of the following using shop code method. We need to find 69 whole cube Before moving on to the solution, let's recall the identity a plus b whole cube is equal to a cube plus 3 a square b plus 3 a b square plus b cube This is the key idea for this question Let's move on to the solution. We need to find 69 whole cube Now consider the number 69. So in the number 69 depends digit say a is equal to 6 and the ones digit Say b is equal to 9 Since in the identity a plus b whole cube, we have four terms a cube, 3 a square b, 3 a b square and b cube So to find the cube of the number 69, we need to make four columns for each of these terms In column 1 we have a cube which is equal to a square into a Then column 2 we have 3 a square b which is written as a square into 3 b then column 3 we have 3 a b square which is written as b square into 3 a Then in column 4 we have b cube which is written as b square into b Now in the first column we need to find a cube that is a square into a that is a is 6 so a square would be 36 into a that is 6 which comes out to be equal to 216 Then next we find out 3 a square b that is a square into 3 b That is a square is 36 into 3 b 3 into 9 27 Which comes out to be equal to 9 7 2 Then next we find out 3 a b square that is b square into 3 a now b square would be 9 into 9 81 into 3 a that is 3 into 6 18 now this would be equal to 1458 Next we have the fourth column that is b2 which has b square into b Now b square is 9 into 9 81 Into b that is 9. So this would be equal to 729 Now after finding the values in each of these four columns What we do is we look at the fourth column first for the value for b cube here is 729 in this number we will underline the unit stitch or the ones digit which is nine and The left over number that is 72 is carry over to the third column and we add this number to the value for 3 a b square that is 1458 on adding this we get 1530 Now in this again we underline the units digit which is 0 and the left over number that is 153 is carried over to the second column and added to the value for 3 a square b That is we have 972 plus 153 this gives us 1 1 2 5 Now here again, we underline the units digit that is 5 and the left over number that is 112 is carried over to the first column and added to the value for a cube So we have 216 plus 112 and this gives us 328 Now we underline this number obtained in the first column that is 328 Now the underlined digits here would give us the required cube of the given number that is 69 cube is equal to 328 5 0 9 That's our final answer is 69 cube is equal to 328 509 So this is how we find the cube of a two digit number using shortcut method this completes the session Hope you understood the solution for this question