Find the hidden rule — 9 * 7 = 32, 13 * 7 = 120, 17 * 9 = 208. Compute 19 * 11.

Introduction / Context:The operator “*” encodes a fixed transformation from two numbers to one number. Find a simple consistent rule that matches all three examples, then apply it to 19 and 11.

Given Data / Assumptions:

• 9 * 7 = 32
• 13 * 7 = 120
• 17 * 9 = 208

Concept / Approach:Test algebraic guesses: a^2 − b^2 works: 9^2 − 7^2 = 81 − 49 = 32; 13^2 − 7^2 = 169 − 49 = 120; 17^2 − 9^2 = 289 − 81 = 208.

Step-by-Step Solution:

Verification / Alternative check:Confirm the rule fits all provided pairs before applying to the new pair, ensuring consistency.

Why Other Options Are Wrong:They do not match the rule a^2 − b^2 for 19 and 11.

Common Pitfalls:

• Trying linear combinations (a ± b) which cannot fit all three examples simultaneously.

Final Answer:240