Question

Karla considers the expression shown in the box.

4x2−9

If she wants to rewrite the boxed expression as an equivalent expression, which choice is correct?

Responses

(2x−3)(2x−3)
( 2 x − 3 ) ( 2 x − 3 )

(2x−3)(2x+3)
( 2 x − 3 ) ( 2 x + 3 )

(4x−9)(x−1)
( 4 x − 9 ) ( x − 1 )

(4x−9)(x+1)
( 4 x − 9 ) ( x + 1 )

Answer 1

The correct way to rewrite the expression 4x^2 - 9 as an equivalent expression is by factoring it into (2x - 3)(2x + 3), which represents the difference of squares.

Step-by-step explanation:

When Karla considers the expression 4x2 - 9, and she wants to rewrite it as an equivalent expression using factoring, she should recognize that the expression is a difference of squares. A difference of squares can be factored into the product of two binomials that are conjugates of each other, meaning they have the same terms but opposite signs. Therefore, the factored form of 4x2 - 9 is (2x - 3)(2x + 3), where 4x2 is factored into (2x)2 and -9 is factored into (-3)2.