 Hello friends, let's discuss the following question. It says, find a plus b whole to the power 4 minus a minus b whole to the power 4. Hence evaluate root 3 plus root 2 whole to the power 4 minus root 3 minus root 2 whole to the power 4. And to solve this question we need to know the expansion of a plus b whole to the power n, which is equal to n c 0 a to the power n plus n c 1 a to the power n minus 1 b. So on the last term will be n c n b to the power n and the expansion of a minus b whole to the power n is given by n c 0 a to the power n minus n c 1 a to the power n minus 1 b plus so on. And the last term will be plus minus 1 to the power n n c n b to the power n. So this knowledge will work as key idea. Let's now start the solution. We have to find a plus b whole to the power 4 minus a minus b whole to the power 4. We first find a plus b whole to the power 4 and we use this expansion where n is 4. So this is equal to 4 c 0 a to the power 4 plus 4 c 1 a to the power 4 minus 1 that is 3 into b plus 4 c 2 a to the power 4 minus 2 that is 2 into b to the power 2 plus 4 c 3 a to the power 4 minus 3 that is 1 into b to the power 3 plus 4 c 4 b to the power 4. We now find a minus b whole to the power 4 using this expansion. It is equal to 4 c 0 a to the power 4 minus 4 c 1 a to the power 4 minus 1 that is 3 into b plus 4 c 2 a to the power 2 into b to the power 2 minus 4 c 3 a to the power 1 b to the power 3 plus minus 1 to the power 4 4 c 4 b to the power 4. Now we find a plus b whole to the power 4 minus a minus b whole to the power 4. a plus b whole to the power 4 is this. So it is 4 c 0 a to the power 4 minus a minus b whole to the power 4 which is this. Now we open the brackets so this becomes equal to when we open the brackets sign will change. So it becomes minus 4 c 0 a to the power 4 plus 4 c 1 a to the power 3 into b minus 4 c 2 a to the power 2 b to the power 2 plus 4 c 3 a into b to the power 3 minus 4 c 4 b to the power 4. Now we see that 4 c 0 a to the power 4 gets cancelled with 4 c 0 a to the power 4. 4 c 2 a to the power 2 b to the power 2 gets cancelled with 4 c 2 a to the power 2 b to the power 2 2 and similarly 4C4 v to the power 4 gets cancelled with 4C4 v to the power 4 and this is equal to twice of 4C1 a to the power 3 into b plus twice of 4C3 a into v to the power 3 and this is again equal to 2 into taking to common 4C1 a to the power 3 into b plus 4C3 a into b to the power 3 and this is equal to 2 into 4C1 is 4 so this term is equal to 4 into a cube b a 4C3 is 4 so this term is equal to 4 into a into b to the power 3 now taking 4 common this is equal to 8 into a cube b plus a b cube hence we have obtained a plus b whole to the power 4 minus a minus b whole to the power 4 is equal to 8 into a cube b plus a b cube now we have to find the value of root 3 plus root 2 whole to the power 4 minus root 3 minus root 2 whole to the power 4 now here a is root 3 and b is root 2 so we substitute the value of a and b here so root 3 plus root 2 whole to the power 4 minus root 3 minus root 2 whole to the power 4 is equal to 8 into root 3 cube into b that is root 2 plus a b cube that is root 3 into root 2 to the power 3 again this is equal to 8 into root 3 cube is 3 root 3 into root 2 plus root 3 into root 2 cube is 2 root so this is equal to 8 into 3 into root 3 into root 2 is root 6 plus 2 into root 3 into root 2 is root 6 again this is equal to 8 into root 6 into 3 plus 2 that is 5 so this is equal to 40 root 6 hence the answer is 8 into a cube b plus a b cube and to the second part answer is 40 root 6 so this completes the question bye for now take care have a good day