(6) \( 49 x^{2} y^{2}-4= \) (7) \( 121 x^{4}-144 b^{6}= \) (8) \( 144 x^{2} y^{4}-81 a^{4} b^{2}= \) (9) \( 49 x^{2}-\frac{9}{16}= \) (1) \( 81 x^{4}-\frac{16}{81} y^{8}= \)

To tackle these expressions, recognizing that they are all examples of the difference of squares can make factoring straightforward and fun! The difference of squares formula, \( a^2 - b^2 = (a + b)(a - b) \), applies here. For instance, in (6), you can factor \( 49x^2y^2 - 4 \) as \( (7xy + 2)(7xy - 2) \), instantly simplifying the problem. In real-world applications, these types of expressions can model various scenarios, such as physics problems involving motion, areas of geometric shapes, or even in finance when calculating differences in quadratic equations. By mastering these factorizations, you’ll not only enhance your algebra skills but also gain tools to tackle problems encountered in fields like engineering and economics!