What is the factored form of n^2 - 25?

1. Identify the form of the expression: The given expression is $n^2 - 25$. This is a binomial expression where both terms are perfect squares. The first term is $n^2$, which is the square of $n$. The second term is $25$, which is the square of $5$. This fits the pattern of a difference of squares: $a^2 - b^2$.
2. Recall the difference of squares formula: The difference of squares formula states that $a^2 - b^2 = (a - b)(a + b)$.
3. Apply the formula: In this case, $a = n$ and $b = 5$. Substituting these values into the difference of squares formula, we get:
$$n^2 - 25 = n^2 - 5^2 = (n - 5)(n + 5)$$
4. Verify the factorization (optional): To verify, we can expand the factored form $(n - 5)(n + 5)$ using the FOIL method (First, Outer, Inner, Last):
First: $n \times n = n^2$
Outer: $n \times 5 = 5n$
Inner: $-5 \times n = -5n$
Last: $-5 \times 5 = -25$
Combining these terms: $n^2 + 5n - 5n - 25 = n^2 - 25$. This matches the original expression.