1. The problem statement, all variables and given/known data Expand and simplify the product of two quaternions: (3 + 2i + 3j + 4k)(3 + 3i + 2j + 5k) Justify your response. 3. The attempt at a solution I have done this by expanding brackets normally, keeping the ijk's in the same order because the multiplication is not commutative. I have the correct answer, I just can't think how to justify it. Why should expanding brackets necessarily work?