Factor. \( \frac{1}{25}-w^{2} \) \( \frac{1}{25}-w^{2}=\square \) (Factor completely.)

To factor \( \frac{1}{25} - w^{2} \), we recognize it as a difference of squares. This can be rewritten as: \[ \left( \frac{1}{5} \right)^{2} - w^{2} = \left( \frac{1}{5} - w \right)\left( \frac{1}{5} + w \right) \] So, \( \frac{1}{25} - w^{2} = \left( \frac{1}{5} - w \right)\left( \frac{1}{5} + w \right) \). Now, if you want to truly embrace the beauty of algebra, think about how this technique can help you simplify expressions and solve equations! Factoring is like unlocking potential; each factor can lead you to different solutions or insights about your mathematical journey. When tackling problems involving differences of squares, it's crucial to remember that they always follow the same formula: \( a^2 - b^2 = (a - b)(a + b) \). One common mistake is overlooking the negative sign, which can lead to incorrect factors. Keep an eye out for those signs!