Coefficient of b in expansion of (3+b)^4

Are you sure you want ONLY the coefficient of b?  If you expand this, you will have b in 3 of 4 terms.

According to Pascal's Triangle, the coefficients of (a+b)^4 are as follows:

                             1
                        1    2    1
                   1      3    3     1
              1       4     6     4     1

So (a+b)^4 would be 1a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

Here, you want (3 + b)^4.  Here's what that looks like:

3^4 + 4[3^3*b] + 6[3^2*b^2] + 4[3*b^3] + 1[b^4]

Which coeff did you want?