 Hello friends. Let's solve the following question. It says expand each of the expressions in exercises 1 to 5 and we are going to discuss the second part. To solve this we need to know the expansion of a minus b whole to the power n. It is equal to nc0 a to the power n minus nc1 a to the power n minus 1 b plus nc2 a to the power n minus 2 b square so on And the last term would be minus 1 to the power n ncn B to the power n. So this knowledge will work as key idea. Let us now move on to the solution the given expression is 2 upon x minus x upon 2 whole to the power 5 It is in the form a minus b whole to the power n and here n is 5 a is 2 upon x and B is x upon 2 now we expand this using the expansion of a minus b whole to the power n so 2 upon x minus x upon 2 whole to the power 5 becomes equal to 5c0 2 upon x to the power 5 minus 5c1 2 upon x to the power 4 Into B. Here B is x upon 2 plus 5c2 into a to the power n minus 2 that is 2 upon x to the power 5 minus 2 that is 3 into b square that means x upon 2 whole square minus 5c3 2 upon x to the power 2 into x upon 2 to the power 3 plus 5c4 2 upon x to the power 1 into x upon 2 to the power 4 plus minus 1 to the power 5 5c5 B to the power 5 that is x upon 2 to the power 5 Again, this is equal to 5c0 is 1. So it is 1 into 2 upon x to the power 5 Minus 5c1 is 5 Into 2 upon x to the power 4 2 to the power 4 is 16 upon x to the power 4 into x upon 2 Plus 5c2 into 2x to the power 3 into x by 2 to the power 2 5c2 is 10 2 to the power 3 is 8 upon x cube Into x square upon 4 Minus 5c3 is 10 into 4 upon x square into x cube upon 8 plus 5c4 is 5 into 2 upon x into x to the power 4 upon 16 Minus 1 to the power 5 is minus 1. So it is minus 5c5 is 1. So it is minus x upon 2 to the power 5 Now this is equal to 2 by x to the power 5 is 32 upon x to the power 5 minus 2 into 8 is 16 1x gets cancelled and it is equal to minus 40 upon x cube plus 4 into 2 is 8 x square gets cancelled and we have 20 upon x minus it is 5 plus 5 upon 8 x cube Minus x upon 2 to the power 5 is x to the power 5 upon 32 Hence the required expansion is 32 x to the power 5 minus 40 upon x cube plus 20 upon x minus 5x plus 5 upon 8 x cube minus x to the power 5 upon 32 So this completes the question. Hope you enjoyed the session. Goodbye and take care