The expression you've written is quite complex, with many terms involving squares and products of differences between coordinates. Let’s break it down for clarity:

The general structure of your equation looks like this:

$\left( (x_{00} - y_{00})^2 + (x_{01} - y_{01})^2 + (x_{10} - y_{10})^2 + (x_{11} - y_{11})^2 \right) \cdot \left( (y_{00} - z_{00})^2 + (y_{01} - z_{01})^2 + (y_{10} - z_{10})^2 + (y_{11} - z_{11})^2 \right)$ $-\left( (x_{00} - z_{00})^2 + (x_{01} - z_{01})^2 + (x_{10} - z_{10})^2 + (x_{11} - z_{11})^2 - \left( (x_{00} - y_{00})^2 + (x_{01} - y_{01})^2 + (x_{10} - y_{10})^2 + (x_{11} - y_{11})^2 + \left( (y_{00} - z_{00})^2 + (y_{01} - z_{01})^2 + (y_{10} - z_{10})^2 + (y_{11} - z_{11})^2 \right)\right)\right)^2$

+ \left( (x_{00} - y_{00})^2 + (x_{01} - y_{01})^2 + (x_{10} - y_{10})^2 + (x_{11} - y_{11})^2 \right) \cdot \left( (y_{00} - z_{00})^2 + (y_{01} - z_{01})^2 + (y_{10} - z_{10})^2 + (y_{11} - z_{11})^2 \right) \right)$$ ### Steps to Simplify: 1. **Group like terms:** Identify common factors to simplify parts of the expression where squares and sums are repeated. 2. **Expand products and powers:** If needed, expand the terms involving products of sums to simplify. 3. **Combine similar terms:** After expansion, combine the terms where possible. 4. **Check for factoring opportunities:** You might notice patterns that allow factoring to simplify the expression further. Would you like me to continue with a detailed step-by-step simplification?