Question

The binary operation * is defined by a * b = a² + b² + ab + 1, then (2 * 3) * 2 is equal to
(a) 20
(b) 40
(c) 400
(d) 445

Answer 1

(d) 445
Given: a * b = a² + b² + ab + 1

$$\begin{gathered} 2*3=2^2+3^2+2\times 3+1 \\ =4+9+6+1 \\ =20 \\ \left(2*3\right)*2=20*2 \\ ={20}^2+2^2+20\times 2+1 \\ =400+4+40+1 \\ =445 \end{gathered}$$