To factor the equation 4x² – 25 = 0, we can recognize that this expression is a difference of squares. The difference of squares can be factored using the identity: a² – b² = (a – b)(a + b).
In our equation, we can identify:
- a² = (2x)², so a = 2x
- b² = 5², so b = 5
Applying the difference of squares formula, we can write:
4x² – 25 = (2x – 5)(2x + 5)
Therefore, the correct factored form of the equation 4x² – 25 = 0 is:
(2x – 5)(2x + 5) = 0
Setting each factor to zero gives the solutions:
- 2x – 5 = 0 ⟹ 2x = 5 ⟹ x = 5/2
- 2x + 5 = 0 ⟹ 2x = -5 ⟹ x = -5/2
This shows how the original quadratic can be factored and also helps find the roots of the equation.