If && is an operation such that for integers a and b we have a && b = a × a + b × b

Question

If && is an operation such that for integers a and b we have a && b = a × a + b × b – a × b, then find (–3) && 2.

Accepted Answer

Given $a \ \&\& \ b = a^2 + b^2 - ab$. For $a = -3$ and $b = 2$, we get: $(-3) \ \&\& \ 2 = (-3)^2 + 2^2 - (-3)(2) = 9 + 4 + 6 = 19$.