Question

Use the Distributive Property to find which expression is equivalent to 9x2−25 .(1 point) Responses (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 left parenthesis 3 x plus 5 right parenthesis squared (3x+5)(3x−5) left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis 9x(x−25)

Answer 1

To find an equivalent expression for $9x^2-25$ using the Distributive Property, we can recognize that this expression is a difference of squares. The difference of squares can be factored using the formula:

$$a^2-b^2=(a+b)(a-b)$$

In this case:

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

So, we can rewrite $9x^2-25$ as:

$$(3x{)}^2-5^2$$

Using the difference of squares formula:

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

Among the response options given, the equivalent expression is:

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

So the correct answer is:

(3x+5)(3x−5)