Question

If the binary operation * on Z is defined by a * b = a² − b² + ab + 4, then value of (2 * 3) * 4 is
(a) 233
(b) 33
(c) 55
(d) −55

Answer 1

(b) 33

Given: a * b = a² − b² + ab + 4
$$\begin{gathered} 2*3=2^2-3^2+2\times 3+4 \\ =4-9+6+4 \\ =5 \\ \left(2*3\right)*4=5*4 \\ =5^2-4^2+5\times 4+4 \\ =25-16+20+4 \\ =33 \end{gathered}$$