Question

If \(a*b=a^3+b^3-3ab\), then \[ \frac{(2*1)*(2*1)}{(2*1)}= \] 

• A. \(1\)
• B. \(3\)
• C. \(9\)
• D. \(27\)

Hint:

For custom operations, always evaluate the inner operation first and then substitute its value into the outer operation.

Answer 1

The Correct Option is C

Concept:
The operation is defined as \[ a*b=a^3+b^3-3ab \] We must first calculate the value of \[ 2*1 \] and then use it in the given expression.

Step 1: Calculate \(2*1\). Using the operation, \[ 2*1=2^3+1^3-3(2)(1) \] \[ =8+1-6 \] \[ =3 \]

Step 2: Calculate \((2*1)*(2*1)\). Since \[ 2*1=3 \] we get \[ (2*1)*(2*1)=3*3 \] Now, \[ 3*3=3^3+3^3-3(3)(3) \] \[ =27+27-27 \] \[ =27 \]

Step 3: Substitute in the expression. \[ \frac{(2*1)*(2*1)}{(2*1)} = \frac{27}{3} \] \[ =9 \]

Step 4: Final answer. \[ \boxed{9} \]