Question

The coefficient of the second term in the expansion of the binomial (4x+3y) to the 3rd power

Answer 1

You can solve this easily by using Pascal's Triangle (look that up if need be).

Here are the first four rows of P. Triangle:

                 1
           1           1
     1          2          1
1        3            3       1
 
 example:  expand (a+b)^3.
 
 Look at the 4th row.  Borrow and use those coefficients:
 
 1a^3 + 3 a^2b + 3ab^2  + b^3

Now expand (4x+3y)^3:

1(4x)^3 + 3(4x)^2(3y)  + 3(4x)*(3y)^2 + (3y)^3

Look at the 2nd term (above):

              3(4x)^2(3y)   can be re-written as 144x^2y.
 
The coeff of the 2nd term is 144.  Note that (4)^2 = 16