9) \( 7-49 a^{2} b^{2} \) h) \( a^{10} 49 b^{2} \) 1) \( \frac{1}{4}-9 \frac{2}{9} \)

Did you know that the expression \( 7 - 49a^{2}b^{2} \) can represent a difference of squares when considering it as a quadratic in a variable? By factoring it, you can rewrite it as \( 7 - (7ab)^{2} \), leading to an exciting transformation that unveils the intersections between algebra and geometry! When it comes to simplifying \( \frac{1}{4} - 9 \frac{2}{9} \), a common mistake is miscalculating the mixed numbers. First, convert \( 9 \frac{2}{9} \) to an improper fraction giving you \( \frac{83}{9} \). You can then find a common denominator of 36, turning \( \frac{1}{4} \) into \( \frac{9}{36} \) and \( \frac{83}{9} \) into \( \frac{332}{36} \). It's all about working systematically to avoid missteps!