Question:
If \( a * b = a^2 – b^2 + ab + 4 \), find:
\[ (2 * 3) * 4 \]
Options:
- (a) 233
- (b) 33
- (c) 55
- (d) -55
Solution:
Step 1: Compute \( 2 * 3 \)
\[ 2 * 3 = 2^2 – 3^2 + (2)(3) + 4 \]
\[ = 4 – 9 + 6 + 4 = 5 \]
Step 2: Compute \( 5 * 4 \)
\[ 5 * 4 = 5^2 – 4^2 + (5)(4) + 4 \]
\[ = 25 – 16 + 20 + 4 = 33 \]
Final Answer:
\[ \boxed{33} \]
Correct Option: (b)