Question

What is the 7th term of (3x + 2y)9?

Answer 1

To get the 7th term of the binomial as written in the given, we first deal with the numerical coefficient of the whole equation and it is given by the equation,
                             nCk = 9C7 
which is equal to 36. 

Then, we deal with the first term of the binomial which is 3x.
                                      (3x)^(n-k) = (3x)^(9-7) = 9x²
Then, we deal with the second term of the binomial which is 2y
                                      (2y)^k = (2y)^(7) = 128y⁷

The answer to this item is the product of the three terms,
                        7th term = (36)(9x²)(128y⁷) = 41472x²y⁷