Peterson Carlson
10/29/2023 · Middle School
14. Factor: \( 9 x^{2}-25 \) \( \begin{array}{l}\text { a }(3 x+5)(3 x-5) \\ \text { b }(-3 x-5)^{2} \\ \text { c }(5 x-3)(5 x+3) \\ \text { d }(3 x-5)^{2}\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To factor the expression \( 9x^2 - 25 \), we can recognize that it is a difference of squares. The difference of squares formula is given by:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify:
- \( a^2 = 9x^2 \) which means \( a = 3x \)
- \( b^2 = 25 \) which means \( b = 5 \)
Now we can apply the difference of squares formula:
\[
9x^2 - 25 = (3x)^2 - 5^2 = (3x - 5)(3x + 5)
\]
Thus, the factored form of \( 9x^2 - 25 \) is:
\[
(3x - 5)(3x + 5)
\]
Looking at the options provided:
- \( \text{a } (3x + 5)(3x - 5) \)
- \( \text{b } (-3x - 5)^2 \)
- \( \text{c } (5x - 3)(5x + 3) \)
- \( \text{d } (3x - 5)^2 \)
The correct answer is:
\[
\text{a } (3x + 5)(3x - 5)
\]
Quick Answer
The correct answer is a. \( (3x + 5)(3x - 5) \).
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