Problem 16 - Entrance Test

Using the identity (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca, here a = -x, b = 2y, c = -3z. (-x + 2y - 3z)^2 = (-x)^2 + (2y)^2 + (-3z)^2 + 2(-x)(2y) + 2(2y)(-3z) + 2(-3z)(-x) = x^2 + 4y^2 + 9z^2 - 4xy - 12yz + 6zx.