Use the Distributive Property to find which expression is equivalent to 9x2−25 .(1 point)

Question

Responses

(3x+5)2
left parenthesis 3 x plus 5 right parenthesis squared

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)

Answer 1

To find the expression equivalent to $9x^2-25$ using the Distributive Property, we recognize that this expression resembles the difference of squares, which is in the form $a^2-b^2$ and can be factored as $(a+b)(a-b)$.

Here, we can identify:

• $a^2=9x^2$ implies $a=3x$
• $b^2=25$ implies $b=5$

Therefore, we can rewrite the expression $9x^2-25$ as:

$$9x^2-25=(3x{)}^2-5^2$$

Using the difference of squares formula, we can factor it:

$$(3x+5)(3x-5)$$

Thus, the expression that is equivalent to $9x^2-25$ is:

$$(3x+5)(3x-5)$$

The correct answer is:

(3x + 5)(3x - 5)