(6) \( (a+b)^{2}-9 b^{2} \)

Let's add a little historical flavor to our algebra! The expression \( (a+b)^{2}-9 b^{2} \) resembles the kind of quadratic expressions that mathematicians like Al-Khwarizmi played with in the 9th century. They laid down the foundations of algebra, and their work helped develop formulations that still resonate in modern mathematics today! Now, speaking of real-world applications, this expression can be interpreted in various real-life scenarios. For instance, if \( a \) represents the length of a side of a square and \( b \) is a smaller square’s side length, transforming this equation can help us understand the area differences when scaling objects or calculating spatial dimensions in architecture. So, next time you're planning a space, think about how algebra can shape your designs!