 Hello friends, let's discuss the following question. It says using binomial theorem evaluate the following. We have to evaluate 96 to the power 3. Now to evaluate 96 to the power 3 we need to know the expansion of a-b whole to the power n. It is given by nc0 a to the power n minus nc1 a to the power n minus 1b plus nc2 a to the power n minus 2b square. So on the last term will be plus minus 1 to the power n ncn b to the power n. So this knowledge will work as key idea. Let us now start the solution. 96 can be written as 100 minus 4. So 96 to the power 3 is equal to 100 minus 4 whole to the power 3. Now we expand this using the expansion of a-b whole to the power n. Now here n is 3, 100 and b is 4. So 96 to the power 3 is equal to 100 minus 4 whole to the power 3. Now this is equal to using expansion 3c0 100 to the power 3 minus 3c1 100 to the power 3 minus 1 that is 2 into b that is 4 plus 3c2 100 to the power 3 minus 2 that is 1 into b square that is 4 to the power 2 minus 3c3 4 to the power 3. Now this is equal to 3c0 is 1. So the first term is 100 to the power 3 which is equal to 1 0 0 0 0 0 minus 3c1 is 3. So the second term is 3 into 100 to the power 2 which is 1 0 0 0 into 4 plus 3c2 is so the third term is 3 into 100 into 4 to the power 2 that is 16 minus 3c3 is 1. So the last term is 4 to the power 3 that is 64. Now this is equal to 1 0 0 0 0 minus 1 lakh 20,000 10,000 into 12 is 1 lakh 20,000 plus 4800 minus 64. Simplifying this we get it to be equal to 8,084,736. Hence 96 cube is equal to 8,084,736. So this completes the question. Hope you enjoyed this session. Goodbye and take care.