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# Which of the following is the correct factored form of the given equation? 4x^{2} - 25 = 0

4x^{2} - 25 = 0

(4x - 5)(x + 5) = 0

(2x - 5)(2x + 5) = 0

2(x - 5)^{2} = 0

**Solution:**

It is given that

4x^{2} - 25 = 0

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

a^{2} - b^{2} = (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 5^{2}

Substituting it in the algebraic identity

(2x)^{2} - 5^{2} = (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? 4x^{2} - 25 = 0

4x^{2} - 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 4x^{2} - 25 = 0 is (2x + 5) (2x - 5).

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