Question:
If \( a * b = a^2 + b^2 + ab + 1 \), find:
\[ (2 * 3) * 2 \]
Options:
- (a) 20
- (b) 40
- (c) 400
- (d) 445
Solution:
Step 1: Compute \( 2 * 3 \)
\[ 2 * 3 = 2^2 + 3^2 + (2)(3) + 1 \]
\[ = 4 + 9 + 6 + 1 = 20 \]
Step 2: Compute \( 20 * 2 \)
\[ 20 * 2 = 20^2 + 2^2 + (20)(2) + 1 \]
\[ = 400 + 4 + 40 + 1 = 445 \]
Final Answer:
\[ \boxed{445} \]
Correct Option: (d)