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

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