Question

If \(a*b=a^2+b^2+ab\), then \[ (1*1)*(1*1)*(1*1)=? \]

• A. \(749\)
• B. \(819\)
• C. \(924\)
• D. \(1048\)

Hint:

Always evaluate custom operations from left to right unless brackets indicate otherwise.

Answer 1

The Correct Option is B

Step 1: Compute \(1*1\). Using \[ a*b=a^2+b^2+ab \] we get \[ 1*1 = 1^2+1^2+1\times1 \] \[ =1+1+1 \] \[ =3 \] Thus, \[ (1*1)*(1*1)*(1*1) = 3*3*3 \]

Step 2: Compute \(3*3\). \[ 3*3 = 3^2+3^2+3\times3 \] \[ =9+9+9 \] \[ =27 \] Now the expression becomes \[ 27*3 \]

Step 3: Compute \(27*3\). \[ 27*3 = 27^2+3^2+27\times3 \] \[ =729+9+81 \] \[ =819 \] Therefore, \[ \boxed{819} \]