Question:
If the binary operation \( * \) on \( \mathbb{Z} \) is defined by:
\[ a * b = a + 3b^2 \]
Find \( 2 * 4 \).
Solution:
Step 1: Substitute \( a = 2 \), \( b = 4 \)
\[ 2 * 4 = 2 + 3(4)^2 \]
Step 2: Simplify
\[ = 2 + 3 \times 16 \]
\[ = 2 + 48 \]
\[ = 50 \]
Final Answer:
\[ \boxed{50} \]