Question
Use the Distributive Property to find which expression is equivalent to 9x^2−25.(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
(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)^2
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
(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)^2
Answers
GPT-4o mini
To find the expression equivalent to \( 9x^2 - 25 \) using the Distributive Property, we recognize that the expression is a difference of squares. This can be factored using the formula for the difference of squares:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In your case, we can rewrite \( 9x^2 - 25 \) as:
\[
(3x)^2 - 5^2
\]
Now applying the difference of squares formula:
\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]
From the provided options, the equivalent expression to \( 9x^2 - 25 \) is:
\[
(3x + 5)(3x - 5)
\]
So the answer is:
\[
(3x + 5)(3x - 5)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In your case, we can rewrite \( 9x^2 - 25 \) as:
\[
(3x)^2 - 5^2
\]
Now applying the difference of squares formula:
\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]
From the provided options, the equivalent expression to \( 9x^2 - 25 \) is:
\[
(3x + 5)(3x - 5)
\]
So the answer is:
\[
(3x + 5)(3x - 5)
\]