If the operation * is defined by a * b = (a × b) + b, what is the value of 5 *…

Concept

A custom binary operation must be evaluated using its stated definition, not the ordinary meaning of its symbol.

Substitute the first operand for a and the second operand for b, then follow the indicated order of operations.

Application

1. Substitute a = 5 and b = 7: 5 * 7 = (5 × 7) + 7.

2. Multiply first: (5 × 7) + 7 = 35 + 7.

3. Add the remaining terms: 35 + 7 = 42.

Cross-check

The definition can also be written as a * b = b(a + 1). Substituting a = 5 and b = 7 gives 7(5 + 1) = 7 × 6 = 42, which agrees with the direct calculation.

Therefore, 5 * 7 = 42.