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

Did you know that the expression \( a^{2}+ab \) pops up quite a bit in algebra and is related to factoring? It's similar to the classic formula for the area of a rectangle! This expression can actually be factored into \( a(a + b) \), which gives you a glimpse into how variables can interact and simplify larger problems in mathematics. In real-world applications, this expression can represent situations in areas like physics, where \( a \) might represent acceleration and \( b \) could be time. By interpreting and factoring expressions like this, we can easily model and solve problems involving motion or growth, making it super useful for practical scenarios!