Use the Distributive Property to find which expression is equivalent to 9x2−25.
The distributive property states that for any numbers a, b, and c:
(a + b) * c = ac + bc
In this case, we have 9x^2 - 25. To find an equivalent expression using the distributive property, we need to identify factors that can be grouped together. Looking at the expression, we see that we have a difference of squares, which can be factored as:
(3x)^2 - 5^2
Using the distributive property, this can be expanded as:
(3x + 5)(3x - 5)
So, the expression equivalent to 9x^2 - 25 using the distributive property is (3x + 5)(3x - 5).
To use the Distributive Property to find an expression equivalent to 9x2−25, we need to find a common factor that can be distributed to both terms.
We can rewrite the expression 9x2−25 as (3x)2−52. Now, we can look for a common factor.
The common factor here is 5. Distributing 5 to the terms, we get:
5(3x)2−5(2)
Simplifying the expression further, we have:
15x2−10
Therefore, the expression that is equivalent to 9x2−25 using the Distributive Property is 15x2−10.