Question
Use the Distributive Property to find which expression is equivalent to 9x^2–25.
A. (3x+5)^2
B. (4.5x+12.5)(4.5x–12.5)
C. (3x+5)(3x–5)
D. 9x(x–25)
A. (3x+5)^2
B. (4.5x+12.5)(4.5x–12.5)
C. (3x+5)(3x–5)
D. 9x(x–25)
Answers
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Answered by
GPT-4o mini
To find the expression equivalent to \( 9x^2 - 25 \) using the Distributive Property, we recognize that this expression is a difference of squares, which follows the formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can rewrite \( 9x^2 - 25 \) as follows:
\[
9x^2 - 25 = (3x)^2 - 5^2
\]
Here, \( a = 3x \) and \( b = 5 \). According to the difference of squares formula, we can factor this expression as:
\[
(3x - 5)(3x + 5)
\]
Now, let's evaluate the options:
A. \( (3x + 5)^2 \) - This is not correct.
B. \( (4.5x + 12.5)(4.5x - 12.5) \) - This does not match our factorization.
C. \( (3x + 5)(3x - 5) \) - This matches our factorization.
D. \( 9x(x - 25) \) - This does not match our factorization.
Therefore, the correct answer is:
**C. \( (3x + 5)(3x - 5) \)**.
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can rewrite \( 9x^2 - 25 \) as follows:
\[
9x^2 - 25 = (3x)^2 - 5^2
\]
Here, \( a = 3x \) and \( b = 5 \). According to the difference of squares formula, we can factor this expression as:
\[
(3x - 5)(3x + 5)
\]
Now, let's evaluate the options:
A. \( (3x + 5)^2 \) - This is not correct.
B. \( (4.5x + 12.5)(4.5x - 12.5) \) - This does not match our factorization.
C. \( (3x + 5)(3x - 5) \) - This matches our factorization.
D. \( 9x(x - 25) \) - This does not match our factorization.
Therefore, the correct answer is:
**C. \( (3x + 5)(3x - 5) \)**.
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