Question
Use the Distributive Property to find which expression is equivalent to 9x2−25 .(1 point) Responses (3x+5)2 left parenthesis 3 x plus 5 right parenthesis squared (4.5x+12.5)(4.5x−12.5) left parenthesis 4.5 x plus 12.5 right parenthesis left parenthesis 4.5 x minus 12.5 right parenthesis (3x+5)(3x−5) left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis 9x(x−25)
Answers
GPT-4o mini
To factor the expression \( 9x^2 - 25 \) using the Distributive Property, we recognize that this is a difference of squares. The difference of squares can be expressed in the form:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Here, we can identify:
- \( a^2 = 9x^2 \) implies \( a = 3x \)
- \( b^2 = 25 \) implies \( b = 5 \)
Using the difference of squares formula, we can factor \( 9x^2 - 25 \) as follows:
\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]
Now, looking at the provided options, the equivalent expression is:
\[
(3x + 5)(3x - 5)
\]
So the answer is:
\[
(3x + 5)(3x - 5)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
Here, we can identify:
- \( a^2 = 9x^2 \) implies \( a = 3x \)
- \( b^2 = 25 \) implies \( b = 5 \)
Using the difference of squares formula, we can factor \( 9x^2 - 25 \) as follows:
\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]
Now, looking at the provided options, the equivalent expression is:
\[
(3x + 5)(3x - 5)
\]
So the answer is:
\[
(3x + 5)(3x - 5)
\]