 Hello and welcome to the session. Let us discuss the following question. It says expand each of the expressions in exercises 1 to 5 and we will be solving 4 exercise. To solve this question we need to know the expansion of A plus B whole to the power n. It is equal to N C 0 A to the power n plus N C 1 A to the power n minus 1 B plus N C 2 A to the power n minus 2 B square so on. And the last term will be N C n B to the power n. So this knowledge will work as k idea. Let us now move on to the solution. The given expression is x upon 3 plus 1 upon x whole to the power 5 which is in the form A plus B whole to the power n where n is 5, A is x upon 3 and B is 1 upon x. Now we expand this using the expansion of A plus B whole to the power n. So x upon 3 plus 1 upon x whole to the power 5 is equal to 5 C 0 A to the power n that is x upon 3 to the power 5 plus 5 C 1 x upon 3 to the power 5 minus 1 that is 4 into B that is 1 upon x plus 5 C 2 x upon 3 to the power 3 into 1 upon x to the power 2 plus 5 C 3 x upon 3 whole to the power 2 into 1 upon x to the power 3 plus 5 C 4 x upon 3 to the power 1 into 1 upon x to the power 4 plus 5 C 5 into B to the power n that is 1 upon x to the power 5. Again this is equal to 5 C 0 is 1. So the first term is x upon 3 to the power 5 plus 5 C 1 is 5 so the second term is 5 into x upon 3 to the power 4 into 1 upon x plus 5 C 2 is n so the third term is n into x upon 3 whole to the power 3 into 1 upon x whole to the power 2 plus 5 C 3 is 10 so the fourth term is 10 into x upon 3 whole to the power 2 into 1 upon x whole to the power 3 plus 5 C 4 is 5 so the fifth term is 5 into x upon 3 into 1 upon x whole to the power 4 plus 5 C 5 is 1 so the last term is 1 upon x to the power 5. Now the first term is x to the power 5 upon 243 as 3 to the power 5 is 243 plus 5 into x to the power 4 upon 81 into 1 upon x plus 10 into x cube upon 27 into 1 upon x square plus 10 into x square upon 9 into 1 upon x cube plus 5 into x upon 3 into 1 upon x to the power 4 plus 1 upon x to the power 5. Now this is equal to x to the power 5 upon 243 plus 5 upon 81 x to the power 3 plus 10 into 27 into x plus 10 upon 9 into 1 upon x that is 10 upon 9 x plus 5 upon 3 into x cube plus 1 upon x to the power 5. Hence the answer is x to the power 5 upon 243 plus 5 upon 81 into x to the power 3 plus 10 upon 27 x plus 10 upon 9 into x plus 5 upon 3 into x cube plus 1 upon x to the power 5. So this completes the version. Hope you enjoyed this session. Goodbye and take care.