Question

4 of 6 Items






Question
Factor completely.

25n2−4

(1 point)
Responses

(n+1)2
open paren n plus 1 close paren squared

(5n+2)(5n−2)
open paren 5 n plus 2 close paren times open paren 5 n minus 2 close paren

(3n+1)(3n−1)
open paren 3 n plus 1 close paren times open paren 3 n minus 1 close paren

(5n−4)2

Answer 1

To factor the expression \(25n^2 - 4\) completely, we can recognize that it is a difference of squares, which follows the formula:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In this case, we can identify:

- \(a = 5n\) (since \((5n)^2 = 25n^2\))
- \(b = 2\) (since \(2^2 = 4\))

Applying the difference of squares formula:

\[
25n^2 - 4 = (5n - 2)(5n + 2)
\]

Thus, the completely factored form of \(25n^2 - 4\) is:

\[
(5n - 2)(5n + 2)
\]

So the correct response is:

**(5n+2)(5n−2)**