Question:
If \( a * b = a^2 + b^2 \), find the value of:
\[ (4 * 5) * 3 \]
Options:
- (a) \( (4^2 + 5^2) + 3^2 \)
- (b) \( (4+5)^2 + 3^2 \)
- (c) \( 41^2 + 3^2 \)
- (d) \( (4 + 5 + 3)^2 \)
Solution:
Step 1: Compute \( 4 * 5 \)
\[ 4 * 5 = 4^2 + 5^2 \]
Step 2: Substitute into expression
\[ (4 * 5) * 3 = (4^2 + 5^2) * 3 \]
Step 3: Apply operation again
\[ = (4^2 + 5^2)^2 + 3^2 \]
So the correct structure matches:
\[ (4^2 + 5^2)^2 + 3^2 \]
Among given options, the closest correct expression form is:
Option (a)
Final Answer:
\[ \boxed{\text{(a)}} \]