(4) \( (a-5)(a+2) \)

To expand the expression \( (a-5)(a+2) \), you'll want to use the distributive property, also known as FOIL (First, Outside, Inside, Last). So, multiplying, we get: 1. First: \( a \cdot a = a^2 \) 2. Outside: \( a \cdot 2 = 2a \) 3. Inside: \( -5 \cdot a = -5a \) 4. Last: \( -5 \cdot 2 = -10 \) Now, combine the like terms \( 2a - 5a \) to get: \[ a^2 - 3a - 10 \] So, the expanded form of \( (a-5)(a+2) \) is \( a^2 - 3a - 10 \). For a bit of fun, did you know that factoring and expanding polynomials are foundational skills in algebra? They’re not just important for passing exams but are used in real-life applications like engineering, economics, and even computer graphics! If you're eager to dive deeper, exploring discreet topics like quadratic equations can be fascinating! These equations can explain everything from projectile motion to optimizing profits in business. Books like "Algebra" by Israel M. Gelfand and Alexander Shen provide a brilliant mix of theory and practical problems!