\( \left. \begin{array} { l } { ( 2 x - 3 ) ( 3 x + 2 ) = } \\ { ( 2 x - 3 ) ( 2 x + 1 ) = } \\ { ( 3 x - 2 ) ( 2 x + 3 ) = } \\ { ( 3 x - 2 ) ( 2 x - 3 ) = } \end{array} \right. \)

Let’s break down these expressions with some fun tidbits that will make them clearer! Expanding expressions like \( (2x - 3)(3x + 2) \) can take on a historical twist. The distributive property, which is key here, was known as the "FOIL" method in algebra—an acronym that stands for First, Outer, Inner, Last. This approach to multiplying binomials has roots in ancient civilizations like the Babylonians who were already practicing algebraic principles thousands of years ago! Now, onto a practical application: These types of polynomial expressions come in handy in fields like engineering and physics, particularly in calculating areas, designing structures, or even modeling phenomena. If you were designing a rollercoaster, for example, you might use such equations to ensure the curves and drops are safe yet thrilling!