Cho (y - z)^2 + (z - x)^2}] + (x - y)^2 = (x + y - 2z)^2

The equations and expressions in your image seem to involve algebraic manipulations, likely within the context of inequalities or geometric interpretations involving three variables \(x\), \(y\), and \(z\).

Here's a breakdown of what you might want to analyze or solve:

1. **Equation Transformation**:
The first expression appears to involve expanding and restructuring sum of squares, leading to a condition involving \(x\), \(y\), and \(z\).

2. **Inequalities**:
The following part of the text seems to involve \(p\) defined as a function of products and squares of the variables. This might suggest using AM-GM inequality or Cauchy-Schwarz inequality to analyze \(p\).

3. **Conditions**:
The note about \(x\), \(y\), and \(z\) not being zero is crucial, as many algebraic identities or inequalities become undefined when any variable is zero.

To proceed, you could consider:
- **Expanding the left-hand side fully** and trying to verify if it simplifies to the right-hand side.
- Analyzing potential conditions under which \(p\) might reach a minimum or maximum based on the values of \(x\), \(y\), and \(z\).

If you have specific questions on any part of it or need help with solving a particular expression, feel free to ask!