1. **Restate the problem:** You asked if $a - c = (a - b)^2 + (b - c)^2$ is true. 2. **Clarify the formula:** The expression $a - c = (a - b)^2 + (b - c)^2$ is actually incorrect. 3. **Correct relationship:** The difference $a - c$ is the sum of the differences $a - b$ and $b - c$, so: $$a - c = (a - b) + (b - c)$$ 4. **Why not squares?** Squaring the differences and then adding does not equal the difference $a - c$ itself. 5. **Example:** If $a - b = 2$ and $b - c = 2$, then: $$a - c = 2 + 2 = 4$$ but $$(a - b)^2 + (b - c)^2 = 2^2 + 2^2 = 4 + 4 = 8$$ which is not equal to $a - c$. 6. **Summary:** The correct formula is addition of differences, not sum of squares.