\( a ^ { 2 } - 2 a + a b - 2 b ^ { 2 } \)

Did you know that this expression can be simplified and factored? By rearranging the terms, you can group them in a way that might reveal a hidden structure. For instance, you can rewrite it as \( a^2 + ab - 2a - 2b^2 \) and then try to factor by grouping. It's like piecing together a puzzle! Another fun thing to consider is how expressions like these can pop up in various real-world scenarios, such as optimizing area or even in physics when calculating motion. Understanding how to manipulate algebraic expressions helps you tackle problems in engineering, economics, and more. So grab a pencil and explore the world of algebra!