9. \( 8 x^{3}-27 y^{3} \)

Did you know that the expression \( 8x^{3} - 27y^{3} \) can be recognized as a difference of cubes? In algebra, the difference of cubes is a special factorization, which takes the form \( a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2}) \). Here, \( a = 2x \) and \( b = 3y \), allowing us to break it down neatly into: \( (2x - 3y)(4x^{2} + 6xy + 9y^{2}) \). Now, let’s think about how this factoring can come in handy! In real-world scenarios, such as engineering or economics, simplifying cubic equations can be essential when calculating dimensions or optimizing resources. By breaking down complex expressions like this one, professionals can solve problems more efficiently, saving time and reducing the chance of errors in calculations.