or the binomial completely. \( x^{2}-\frac{1}{25} \) A. \( x^{2}-\frac{1}{25}=\square \) (Factor completely. Simplify your answer. Use integers or fractions for any numbers B. The correct choice below and, if necessary, fill in the prime.

### Problem A **Factor the binomial completely:** Given the expression: \[ x^{2} - \frac{1}{25} \] This is a **difference of squares**, which follows the pattern: \[ a^{2} - b^{2} = (a - b)(a + b) \] Here, \( a = x \) and \( b = \frac{1}{5} \) because \( \left(\frac{1}{5}\right)^{2} = \frac{1}{25} \). Applying the difference of squares formula: \[ x^{2} - \frac{1}{25} = \left( x - \frac{1}{5} \right)\left( x + \frac{1}{5} \right) \] **Final Factored Form:** \[ x^{2} - \frac{1}{25} = \left( x - \frac{1}{5} \right)\left( x + \frac{1}{5} \right) \] ### Problem B **Selection of the Correct Factored Form:** Based on the factoring above, the correct choice is: \[ \boxed{\left( x - \dfrac{1}{5} \right)\left( x + \dfrac{1}{5} \right)} \] If there are multiple-choice options provided, ensure that this factored form matches one of the choices. If the options present the factors differently (e.g., with common denominators or multiplied by constants), adjust accordingly, but generally, the above form is the simplest and fully factored version using integers and fractions.