Factor completely.

16n2–49

1 answer

The expression \( 16n^2 - 49 \) is a difference of squares. It can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \).

In this case:

  • \( a^2 = 16n^2 \) implies \( a = 4n \)
  • \( b^2 = 49 \) implies \( b = 7 \)

Now, applying the difference of squares formula:

\[ 16n^2 - 49 = (4n)^2 - 7^2 = (4n - 7)(4n + 7) \]

Thus, the complete factorization of \( 16n^2 - 49 \) is:

\[ \boxed{(4n - 7)(4n + 7)} \]