Which of the following is the correct factored form of the given equation? 4x² - 25 = 0
4x² - 25 = 0
(4x - 5)(x + 5) = 0
(2x - 5)(2x + 5) = 0
2(x - 5)² = 0

Solution:

It is given that

4x² - 25 = 0

In order to factorize it, we can make use of the algebraic identity

a² - b² = (a + b) (a - b) is the difference of squares.

We know that

(4x)² can be written as (2x)²

25 can be written as 5²

Substituting it in the algebraic identity

(2x)² - 5² = (2x + 5) (2x - 5)

So the factored form is (2x + 5) (2x - 5).

Therefore, the factored form of the given equation is (2x + 5) (2x - 5).

Which of the following is the correct factored form of the given equation? 4x² - 25 = 0
4x² - 25 = 0
(4x - 5)(x + 5) = 0
(2x - 5)(2x + 5) = 0
2(x - 5)² = 0

Summary:

The correct factored form of the given equation 4x² - 25 = 0 is (2x + 5) (2x - 5).