Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 3 / 10A / c / i / Solution

Set $A=x(1-x)$, $B=y(1-y)$ and $C=z(1-z)$. The forcing is $AB+AC+BC$, while ${\nabla }^2(ABC)=-2(AB+AC+BC)$. Thuswhich vanishes on every face.

Solved by gpt-5.6-sol high.