 Hi, and how are you all today? The question says, find the coefficient of a raised to the power 5 and b raised to the power 7 in a minus 2b raised to the power 12. As, first of all, to find out the coefficient we need to convert this binomial expansion in its general term, we can write a minus 2b raised to the power 12 as a plus minus 2b the whole raised to the power 12. Right? Now, the general term, t r plus 1 can be written as 12cr a raised to the power 12 minus r and minus 2b raised to the power r. Right? Now, on putting 12 minus r equals to 5 because we need to find out the coefficient of a raised to the power 5 and and solving this linear equation, we have the value of r as 12 minus 5 that is equal to 7. Now, we have t r plus 1th term as 12c7 a raised to the power 5 minus 2 raised to the power 7 and b raised to the power 7. This can be split to the further. 12 factorial divided by 7 factorial multiplied by 5 factorial into minus 2 raised to the power 7 into a raised to the power 5, b raised to the power 7. Further, on solving it, we have 12 into 11, 10, 9, 8 into 7 factorial can be written as and divided by 7 factorial into 5 factorial can be written as 5 into 4 into 3 into 2 into 1. Further, minus 2 raised to the power 7 can be written as 128 and this is multiplied by a raised to the power 5 and b raised to the power 7. On solving it and simplifying, we have left with 11 into 9 into 8 into 128 into a raised to the power 5, b raised to the power 7 can be written as 101376 a raised to the power 5, b raised to the power 7. So, clearly we can see that coefficient of a raised to the power 5, b raised to the power 7 in the binomial expansion of a minus 2b raised to the power 12 is this whole term that is 101376. Right? So, this is our required answer to the second question. I hope you enjoyed this session. Do remember your general term. Take care.