1. **State the problem:** Explain how to factor the expression $x^2 - 25$ into $(x - 5)(x + 5)$. 2. **Recall the difference of squares formula:** For any two terms $a$ and $b$, the difference of squares is given by: $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Identify $a$ and $b$ in $x^2 - 25$:** - Here, $a = x$ because $x^2 = (x)^2$. - And $b = 5$ because $25 = 5^2$. 4. **Apply the formula:** $$x^2 - 25 = x^2 - 5^2 = (x - 5)(x + 5)$$ 5. **Explanation:** - This works because when you multiply $(x - 5)(x + 5)$, you get: $$x \times x + x \times 5 - 5 \times x - 5 \times 5 = x^2 + 5x - 5x - 25 = x^2 - 25$$ - The middle terms $+5x$ and $-5x$ cancel out, leaving the difference of squares. 6. **Summary:** - The expression $x^2 - 25$ is a difference of squares and factors into $(x - 5)(x + 5)$ by applying the difference of squares formula.