3. \( (2 n+3)(n-2) \)

To expand the expression \( (2n + 3)(n - 2) \), you can use the distributive property (commonly called the FOIL method for binomials). Start by multiplying each term in the first parentheses by each term in the second parentheses: 1. \( 2n \cdot n = 2n^2 \) 2. \( 2n \cdot (-2) = -4n \) 3. \( 3 \cdot n = 3n \) 4. \( 3 \cdot (-2) = -6 \) Now, combine all these products: \[ 2n^2 - 4n + 3n - 6 \] Simplifying the middle terms results in: \[ 2n^2 - n - 6 \] So, the final expanded form of \( (2n + 3)(n - 2) \) is \( 2n^2 - n - 6 \). --- A fun fact about polynomials is that they can be found in many real-world applications! For example, in physics, the trajectory of a projectile can often be modeled by quadratic equations, which are a specific type of polynomial. Understanding how to manipulate these expressions can help predict the path of flying objects and even the design of roller coasters! When working with polynomials, a common mistake is forgetting to combine like terms after expansion. Always double-check your work to ensure you’ve simplified the expression properly. Missing out on combining the terms can lead to incorrect answers, and it’s an easy step to overlook.