Question

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

Answer 1

The coefficients of a binomial expansion are determined by the Pascal's triangle.

Take a look at the picture.

draw the Pascal's triangle up to the third row. (the row with only 1 is the zero'th row)

Also, notice that as we expand $(A+B) ^{3}$,
in each term the power of A decreases by 1, starting from 3, and the powers of B increase by 1, up to 3.

According to these, the second term of $(A+B) ^{3}$ is 
$3A^{2}B$, 

where A=4x, and B=3y,

substituting A an B:

$3A^{2}B=3(4x)^{2}(3y)=3*16 x^{2} *3y=144 x^{2} y$

Answer: 144