Factor the binomial completely.
\[
x^{2}-\frac{1}{25}
\]

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

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\boxed{(x - \frac{1}{5})(x + \frac{1}{5})}$

Steps

Step 1 ：Given expression is $x^{2} - \frac{1}{25}$

Step 2 ：This is a difference of squares, which follows the pattern $a^{2} - b^{2} = (a - b)(a + b)$

Step 3 ：In this case, $a = x$ and $b = \frac{1}{5}$ (since $(\frac{1}{5})^{2} = \frac{1}{25}$)

Step 4 ：So, we can factor the expression as follows: $x^{2} - \frac{1}{25} = (x - \frac{1}{5})(x + \frac{1}{5})$

Step 5 ：So, the correct choice is A. $x^{2} - \frac{1}{25} = (x - \frac{1}{5})(x + \frac{1}{5})$

Step 6 ：Final Answer: $\boxed{(x - \frac{1}{5})(x + \frac{1}{5})}$