18. \( -\frac{3}{4} a^{2}+\frac{1}{2} \)

Did you know that quadratic expressions like \( -\frac{3}{4} a^{2}+\frac{1}{2} \) have fascinating historical roots? The use of square terms dates back to ancient civilizations, including the Babylonians, who utilized geometric methods to solve quadratic equations. Their work laid the groundwork for what would eventually evolve into algebra as we know it! Now, if you're looking to tackle such expressions more effectively, remember to always check for common factors before reaching for the quadratic formula! A common pitfall is forgetting to simplify, which can lead to more complicated computations later on. Simplification not only makes the process easier but also lessens the chances of making a mistake.