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)
The expression that is equivalent to 9x^2 - 25 using the Distributive Property is (3x+5)(3x-5).
To use the distributive property to find the expression equivalent to 9x^2 - 25, you need to factor the expression.
The distributive property states that for any numbers a, b, and c, a(b + c) is equivalent to ab + ac.
In this case, we have 9x^2 - 25, which can be rewritten as (3x)^2 - 5^2.
Now, we can apply the distributive property by factoring the expression as the difference of two squares:
(3x + 5)(3x - 5).
Therefore, the expression equivalent to 9x^2 - 25 using the distributive property is (3x + 5)(3x - 5).
To use the Distributive Property, you need to distribute each term of one expression to every term of the other expression within the parentheses.
The given expression is 9x^2 - 25.
Let's apply the Distributive Property:
(4.5x + 12.5)(4.5x - 12.5)
= (4.5x)(4.5x) + (4.5x)(-12.5) + (12.5)(4.5x) + (12.5)(-12.5)
= 20.25x^2 - 56.25x + 56.25x - 156.25
= 20.25x^2 - 156.25
(3x + 5)^2
= (3x + 5)(3x + 5)
= (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)
= 9x^2 + 15x + 15x + 25
= 9x^2 + 30x + 25
(3x + 5)(3x - 5)
= (3x)(3x) + (3x)(-5) + (5)(3x) + (5)(-5)
= 9x^2 - 15x + 15x - 25
= 9x^2 - 25
9x(x - 25)
= 9x^2 - 225x
Therefore, the expression equivalent to 9x^2 - 25 using the Distributive Property is (3x + 5)(3x - 5).