A binary operation ★ on natural numbers is defined by a ★ b = a2 + b2 − ab.…

Concept

A binary operation assigns a unique output to an ordered pair of inputs by a fixed rule.

To evaluate a defined operation, substitute the two inputs for a and b in the rule, then follow the usual order of arithmetic.

Application

1. Use a = 9 and b = 10 in a ★ b = a2 + b2 − ab.

2. 9 ★ 10 = 92 + 102 − (9 × 10).

3. = 81 + 100 − 90.

4. = 181 − 90 = 91.

Cross-check

The formula is symmetric in a and b, so swapping the inputs must give the same output. Thus 102 + 92 − (10 × 9) = 100 + 81 − 90 = 91, which confirms the calculation.

Therefore, the value of 9 ★ 10 is 91.