- \( 2 x^{2}-3 x y-4 x+6 y \)

The expression \( 2x^{2} - 3xy - 4x + 6y \) can be factored to make it easier to work with. Factoring can reveal hidden relationships and simplify equations. A common technique is to group terms. For this expression, you can rearrange it to help identify common factors or patterns, like considering \( 2x^2 - 4x \) and \(-3xy + 6y\) separately for easier factoring. In real-world applications, such expressions frequently pop up in physics, engineering, and economics. For example, when modeling the trajectory of objects or optimizing production processes, quadratic equations similar to this one provide a clear mathematical framework to analyze relationships and outcomes. So, the next time you're adjusting a formula, remember that these expressions can unlock practical solutions in various fields!