 Hi, and how are you all today? The question says find the middle terms in the expansion of 3 minus x cubed divided by 6 raised to the power 7. Before proceeding on with the solution, whenever we need to find the middle term of an expansion that is e plus p raised to the power n, if n is an odd number, there will be two middle terms. One will be n plus 1 divided by 2 th term and the other will be n plus 1 divided by 2 plus 1 th term. These are the middle terms when n is an odd number. The knowledge of the middle terms are the key idea of our question. Let us proceed on with our solution. Now here the expression which is given to us is 3 minus x divided by 6 x cubed divided by 6 raised to the power 7. Now here n is an odd number that is equal to 7. So the middle terms is equal to 7 plus 1 th 1 by 2 th term and 7 plus 1 by 2 plus 1 th term that is the fourth and the fifth term. So what we need to do next, we need to find out t4 and t5. If you are finding out t4 that means we can write it down as 3 plus 1 and here it can be written as 4 plus 1 right. Now on substituting the values that is a is equal to 3, b is equal to minus x cubed raised to the power divided by 6, n is equal to 7 and for this r is equal to 3 whereas here also the values of a, b and n will remain the same but the value of r will change to 4. Moving on further let us find out. Now here t4 will be equal to 7 c3 3 raised to the power 7 minus 3 minus x cubed divided by 6 raised to the power 3 which can be solved further that is 7 factorial divided by 3 factorial multiplied by 4 factorial 3 raised to the power 4 can be written as e t1 and here we have minus 1 raised to the power 3 where x cubed divided by 6 raised to the power 3. Similarly here we can find out t5 in the same manner we have 7 c4 3 raised to the power 7 minus 4 minus x cubed divided by 6 raised to the power 4 that is equal to 7 factorial divided by 3 factorial multiplied by 4 factorial 3 raised to the power 3 minus 1 raised to the power 4 x cubed raised to the power 6 divided by 4 further down to the solution it should be on solving this whole thing we have minus 105 x raised to the power 9 divided by 8 as t4 and here t5 is equal to the answer that is 35 divided by 48 x raised to the power 12. The middle terms of the expansion are minus 105 divided by 8 x raised to the power 9 and 35 divided by 48 x raised to the power 12. This ends the session I hope you enjoyed the session take care.