Question
Use the Distributive Property to find which expression is equivalent to 9x2−25 .(1 point) Responses
A. 9x(x−25)
B.(4.5x+12.5)(4.5x−12.5)
C. (3x+5)(3x−5)
D. (3x+5)^2
A. 9x(x−25)
B.(4.5x+12.5)(4.5x−12.5)
C. (3x+5)(3x−5)
D. (3x+5)^2
Answers
GPT-4o mini
To find an equivalent expression for \(9x^2 - 25\) using the Distributive Property, we can recognize that \(9x^2 - 25\) can be factored as a difference of squares. The difference of squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In our expression \(9x^2 - 25\):
- \(a^2 = 9x^2\) which means \(a = 3x\)
- \(b^2 = 25\) which means \(b = 5\)
Using the difference of squares formula, we can factor \(9x^2 - 25\) as follows:
\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]
Now let's check the options provided:
- A. \(9x(x - 25)\) (not correct)
- B. \((4.5x + 12.5)(4.5x - 12.5)\) (not correct)
- C. \((3x + 5)(3x - 5)\) (this matches what we found)
- D. \((3x + 5)^2\) (not correct)
The correct equivalent expression is:
**C. (3x + 5)(3x - 5)**
\[
a^2 - b^2 = (a - b)(a + b)
\]
In our expression \(9x^2 - 25\):
- \(a^2 = 9x^2\) which means \(a = 3x\)
- \(b^2 = 25\) which means \(b = 5\)
Using the difference of squares formula, we can factor \(9x^2 - 25\) as follows:
\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]
Now let's check the options provided:
- A. \(9x(x - 25)\) (not correct)
- B. \((4.5x + 12.5)(4.5x - 12.5)\) (not correct)
- C. \((3x + 5)(3x - 5)\) (this matches what we found)
- D. \((3x + 5)^2\) (not correct)
The correct equivalent expression is:
**C. (3x + 5)(3x - 5)**