 Hi 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 the first question. Now to expand this expression we need to know the expansion of A-B whole to the power n. It is equal to nC0 A to the power n minus nC1 A to the power n minus 1B plus nC2 A to the power n minus 2 B to the power 2 so on and the last term will be minus 1 to the power n nCn B to the power n. So this knowledge will work as the idea. Let us now proceed on with the solution. The given expression is 1 minus 2x whole to the power 5 and it is in the form A minus B whole to the power n where n is 5, A is 1, B is 2x. Now we expand this using the expansion of A minus B whole to the power n. So 1 minus 2x whole to the power 5 is equal to 5C0 1 to the power 5 since A is 1. So the first term is 5C0 1 to the power 5 minus 5C1 A to the power n minus 1 that is 1 to the power 5 minus 1 that is 4 into B which is 2x plus 5C2 1 to the power 3 into 2x to the power 2 minus 5C3 1 to the power 2 and 2x to the power 3 plus 5C4 1 to the power 1 into 2x to the power 4 and the last term is plus minus 1 to the power 5 into 5C5 into 2x to the power 5. Now we simplify this 5C0 is 1 so the first term is 1 minus 5C1 is 5 so the second term is 5 into 2x plus 5C2 is 10 so second term is 10 into 2x whole square is 4x square minus 5C3 is 10 so the fourth term is 10 into 2x whole cube which is equal to 8x cube plus 5C4 is 5 into 2x to the power 4 which is 16x to the power 4 minus 1 to the power 5 is minus 1 so this is equal to minus 5C5 is 1 into 2x to the power 5 is 32x to the power 5 now this is equal to 1 minus 10x plus 40x square minus 80x cube plus 80x to the power 4 minus 32x to the power 5 and this is the required expansion so the expansion of 1 minus 2x whole to the power 5 is 1 minus 10x plus 40x square minus 80x cube plus 80x to the power 4 minus 32x to the power 5 so this concludes the question hope you enjoyed the session goodbye and take care