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