2. Find the coefficient of \( b \) in expansion of \( (3+b)^{4} \)

To find the coefficient of \( b \) in the expansion of \( (3+b)^{4} \), we can use the binomial theorem, which states that: \[ (x+y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k \] In our case, \( x = 3 \), \( y = b \), and \( n = 4 \). We are looking for the term where \( k = 1 \), since this term will contain \( b \). The general term in the expansion is given by: \[ \binom{4}{k} (3)^{4-k} (b)^k \] For \( k = 1 \): \[ \text{Term} = \binom{4}{1} (3)^{4-1} (b)^1 = 4 \cdot 3^3 \cdot b \] Calculating \( 3^3 \): \[ 3^3 = 27 \] Now substituting it back: \[ \text{Term} = 4 \cdot 27 \cdot b = 108b \] So, the coefficient of \( b \) in the expansion of \( (3+b)^{4} \) is \( \boxed{108} \).