 Hello friends, let's solve the following question. It says, expand each of the expressions in exercises 1 to 5 and we'll be solving the third question. To solve this question we need to know the binomial expansion of a-b whole to the power n. It is equal to mc0 a to the power n minus mc1 a to the power n minus 1b plus mc2 a to the power n minus 2 b square. So on the last term will be minus 1 to the power n mcn b to the power n. So this is the key idea. Let us now move on to the solution. The given expression is 2x minus 3 whole to the power 6 and it is in the form a minus b whole to the power n where n is 6, a is 2x and b is 3. Now we expand this using the expansion of a minus b whole to the power n. So 2x minus 3 whole to the power 6 is equal to 6c0 2x to the power 6 minus 6c1 2x to the power 6 minus 1 that is 5 into b that is 3 plus 6c2 2x to the power 4 into b square that is 3 square minus 6c3 2x to the power 3 into 3 to the power 3 plus 6c4 2x to the power 2 into 3 to the power 4 minus 6c5 into 2x to the power 1 into 3 to the power 5 plus minus 1 to the power 6 6c6 3 to the power 6. Again this is equal to 6c0 2x to the power 6 is 64x to the power 6 minus 6c1 2x to the power 5 is 32x to the power 5 into 3 plus 6c2 2x to the power 4 is 16x to the power 4 into 9 minus 6c3 into 8xq into 27 plus 6c4 into 4x square and 3 to the power 4 is 81 minus 6c5 into 2x into 3 to the power 5 3 to the power 5 is 243 plus minus 1 to the power 6 is 1 into 6c6 3 to the power 6 is 729. Again this is equal to 6c0 is 1 so the first term is 64x to the power 6 and 6c1 is 6 so the second term is 6 into 32x to the power 5 into 3 plus 6c2 is 15 so second term is 15 into 16x to the power 4 into 9 minus 6c3 is 20 so the fourth term is 20 into 8xq into 27 plus 64 is 15 so the fifth term is 15 into 4x square into 8 minus 6c5 is 6 so the sixth term is 6 into 2x into 243 and the last term is 6c6 is 1 so it is 1 into 729 which is 729. Now this becomes equal to 64x to the power 6 minus 576x to the power 5 plus 2160x to the power 4 minus 4320x to the power 3 plus 4860x to the power 2 minus 2916x plus 729 so this is the required expansion. This is the required answer and this completes the question. Hope you enjoyed this session. Goodbye and take care.