 Hi Ian, how are you all today? I am Priyanka and let us discuss this question says find the coefficient of x raised to the power 5 in x plus 3 raised to the power 8. Now before proceeding on with the solution we must be well versed with the general term of this binomial expansion. Now the general term of r plus one-th term in this expansion is written as ncr a raised to the power n minus r b raised to the power r and if we are finding out the coefficient of x raised to the power a raised to the power n minus r that will be ncr this term multiplied by b raised to the power r right. So the knowledge of the general term as well as the coefficient is the key idea of this question. Let us proceed on with our solution and here we need to find out coefficient of x raised to the power 5 in x plus 3 raised to the power 8. Now first of all we will be converting or we will be writing the general term of this expansion. For writing the general term of this expansion we must know what is a, b and n of this equation. Here a is x, b is 3 and n is 8. So on substituting a, b and n in this form we have x raised to the power 8 minus r multiplied by 3 raised to the power r. Now we need to find out the coefficient of x raised to the power 5. For that 8 minus r should be equal to 5 right that means r is equal to 8 minus 5 that is equal to 3. So the value of r should be equal to 3. Now on substituting the value of r as 3 in equation 1 that is this we have general term is equal to 8c3 x raised to the power 5 3 raised to the power 3. Now we can easily write down the coefficient of x raised to the power 5 that is 8c3 multiplied by 3 raised to the power 3. Let us simplify it. It can be written as 8 factorial divided by 3 factorial multiplied by 5 factorial multiplied by 3 raised to the power 3 means 27. Now we can write 8 factorial as 8 into 7 into 6 into 5 factorial divided by 3 factorial can be written as 3 into 2 into 1 and 5 factorial will get cancelled out and it should be multiplied by 27. Further 3 and 2 will get cancelled out with the 6 in the numerator and we are left with 8 into 7 into 27 that is equal to 1512. So the answer of this question is the coefficient of x raised to the power 5 in x plus 3 raised to the power 8 is 1512. So this is our final answer. I hope you enjoyed this session. Do remember how to write down the general term as well as the coefficient of the variables. Bye for now.