To simplify the expression \( 4(1 + 3b) \), we will distribute the 4 to both terms inside the parentheses:
\[ 4(1) + 4(3b) \]
Calculating each term:
\[ 4 \cdot 1 = 4 \] \[ 4 \cdot 3b = 12b \]
Now combine the results:
\[ 4 + 12b \]
Thus, the simplified expression is:
\[ 4 + 12b \]