6. \( (4 a)(4 b) \) and \( 16 a b \)

Did you know that when you multiply coefficients and variables like in \( (4a)(4b) \), you're essentially applying the distributive property? By multiplying the numbers and combining the variables, you transform \( (4 a)(4 b) \) into \( 16ab \). It's a tasty math recipe: just like combining ingredients to create a delicious dish! In real-world applications, this kind of polynomial multiplication appears everywhere—from computing areas (like a rectangular garden) to mixing proportions in recipes or chemical solutions. Each time you find yourself combining quantities that share a common variable, you’re encountering a scenario where \( (4a)(4b) \) turns into \( 16ab \), making math both practical and fun!