Question
Use the Distributive Property to find which expression is equivalent to 9x2−25 .(1 point)
Responses
9x(x−25)
9 x left parenthesis x minus 25 right parenthesis
(3x+5)(3x−5)
left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis
(3x+5)2
left parenthesis 3 x plus 5 right parenthesis squared
(4.5x+12.5)(4.5x−12.5)
Responses
9x(x−25)
9 x left parenthesis x minus 25 right parenthesis
(3x+5)(3x−5)
left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis
(3x+5)2
left parenthesis 3 x plus 5 right parenthesis squared
(4.5x+12.5)(4.5x−12.5)
Answers
GPT-4o mini
To solve for an expression equivalent to \( 9x^2 - 25 \) using the Distributive Property, we can recognize that this expression resembles the difference of squares. Specifically, it can be factored using the identity \( a^2 - b^2 = (a - b)(a + b) \).
In this case, we can identify \( 9x^2 \) as \( (3x)^2 \) and 25 as \( 5^2 \). Thus, we rewrite it as:
\[
9x^2 - 25 = (3x)^2 - 5^2
\]
Applying the difference of squares formula:
\[
(3x - 5)(3x + 5)
\]
So, the expression that is equivalent to \( 9x^2 - 25 \) is:
\[
(3x + 5)(3x - 5)
\]
Which corresponds to the second option in your responses:
**(3x + 5)(3x - 5)**.
In this case, we can identify \( 9x^2 \) as \( (3x)^2 \) and 25 as \( 5^2 \). Thus, we rewrite it as:
\[
9x^2 - 25 = (3x)^2 - 5^2
\]
Applying the difference of squares formula:
\[
(3x - 5)(3x + 5)
\]
So, the expression that is equivalent to \( 9x^2 - 25 \) is:
\[
(3x + 5)(3x - 5)
\]
Which corresponds to the second option in your responses:
**(3x + 5)(3x - 5)**.