1. **State the problem:** Factor the expression $25x - 75y + 25$. 2. **Identify the greatest common factor (GCF):** The coefficients are 25, -75, and 25. The GCF of 25, 75, and 25 is 25. 3. **Factor out the GCF:** $$25x - 75y + 25 = 25(x - 3y + 1)$$ 4. **Explain:** We took 25 out of each term because 25 divides evenly into all coefficients. Inside the parentheses, each term is divided by 25, resulting in $x$, $-3y$, and $1$. 5. **Final answer:** $$25(x - 3y + 1)$$