Question
Which expression is equivalent to 9n² - 25?
Q
Η 9(n-4)2
G (3n + 5)(3n - 5)
J 9(n + 4)(n - 4)
F (3n-5)² 2
Q
Η 9(n-4)2
G (3n + 5)(3n - 5)
J 9(n + 4)(n - 4)
F (3n-5)² 2
Answers
GPT-4o mini
To determine which expression is equivalent to \( 9n^2 - 25 \), we can recognize that this is a difference of squares. The difference of squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can rewrite \( 9n^2 - 25 \) as:
\[
(3n)^2 - 5^2
\]
Here, \( a = 3n \) and \( b = 5 \). Applying the difference of squares formula, we have:
\[
9n^2 - 25 = (3n - 5)(3n + 5)
\]
Now, we will look at the options provided:
- Q: \( 9(n-4)^2 \)
- H: \( (3n + 5)(3n - 5) \)
- J: \( 9(n + 4)(n - 4) \)
- F: \( (3n - 5)^2 \)
The expression that matches our factorization is:
**H: \( (3n + 5)(3n - 5) \)**
Therefore, the correct answer is:
**H**
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can rewrite \( 9n^2 - 25 \) as:
\[
(3n)^2 - 5^2
\]
Here, \( a = 3n \) and \( b = 5 \). Applying the difference of squares formula, we have:
\[
9n^2 - 25 = (3n - 5)(3n + 5)
\]
Now, we will look at the options provided:
- Q: \( 9(n-4)^2 \)
- H: \( (3n + 5)(3n - 5) \)
- J: \( 9(n + 4)(n - 4) \)
- F: \( (3n - 5)^2 \)
The expression that matches our factorization is:
**H: \( (3n + 5)(3n - 5) \)**
Therefore, the correct answer is:
**H**