Question

what is the factored form of $n^2 - 25$?
$(n - 25)(n - 1)$
$(n - 5)(n + 5)$
$(n + 5)(n + 5)$
$(n - 25)(n + 1)$

Explanation:

Step1: Recognize difference of squares

The expression $n^2 - 25$ is a difference of squares, where $n^2 = (n)^2$ and $25 = 5^2$. The formula for factoring a difference of squares is $a^2 - b^2 = (a-b)(a+b)$.

Step2: Apply the formula

Substitute $a = n$ and $b = 5$ into the difference of squares formula:
$n^2 - 5^2 = (n - 5)(n + 5)$

Step3: Match with options

Compare the result to the given multiple-choice options.

Answer:

(n - 5)(n + 5)