The problem asks to expand the expression $(x - 2y + 3z)^2$.

1. Problem Description

The problem asks to expand the expression $(x - 2y + 3z)^2$.

2. Solution Steps

We need to expand the square of the trinomial $(x - 2y + 3z)$. We can use the formula:

$(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$.

In our case, $a=x$, $b=-2y$, and $c=3z$.

So, we have:

$(x - 2y + 3z)^2 = (x)^2 + (-2y)^2 + (3z)^2 + 2(x)(-2y) + 2(x)(3z) + 2(-2y)(3z)$

$= x^2 + 4y^2 + 9z^2 - 4xy + 6xz - 12yz$

3. Final Answer

The expanded form of $(x - 2y + 3z)^2$ is $x^2 + 4y^2 + 9z^2 - 4xy + 6xz - 12yz$.