 Hi and how are you all today? The question says, find the fourth term in the expansion of x-2y raised to the power 12. We need to find the fourth term. Let us start with our solution. In the hair, the given binomial expression is x-2y raised to the power 12. We know that general term of r plus one-th term is equal to ncr a raised to the power n minus r v raised to the power r. Now here if you compare a is equal to x whereas this can be written as further x plus minus 2y the whole raised to the power 12. So if you compare we have x as a v as minus 2y and n as 12. Now here we need to find the fourth term in the binomial expression x minus 2y raised to the power 12. So fourth term of the expression will be written as t 3 plus 1. That means here our r is equal to 3. Right, now just substitute the values we have 12c3 x raised to the power 12 minus 3 minus 2y raised to the power 3. Let us simplify it. We have 12 factorial divided by 3 factorial into 9 factorial x raised to the power 9 minus 1 raised to the power 3, 2 raised to the power 3 and y raised to the power 3. Let us simplify it and we have x raised to the power 9 minus 1 raised to the power 3 means minus 1 itself, 2 raised to the power 3 means 8 and y raised to the power 3 means y the whole cube. Simplify and we have minus 220 that is 2 into 1120, 2 into 10, 220 with a minus sign into 8 x raised to the power 9 and y raised to the power 3 which is further equal to minus 1760 x raised to the power 9 and y raised to the power 3 and hence the answer to this session is that is the fourth term is minus 1760 x raised to the power 9 y raised to the power 3. This is the fourth term of the binomial expansion of x minus 2y raised to the power 12. So this is how we can find any term of an expansion. Take care. Bye for now.