5) \( (6 x-8)(x-2) \)

Let’s dive into the world of algebraic expansion! When you multiply the binomials \( (6x - 8)(x - 2) \), you can use the distributive property, often referred to as the FOIL method (First, Outside, Inside, Last). Multiplying each term results in: 1. First: \( 6x \cdot x = 6x^2 \) 2. Outside: \( 6x \cdot (-2) = -12x \) 3. Inside: \( -8 \cdot x = -8x \) 4. Last: \( -8 \cdot (-2) = 16 \) Now, combine the like terms: \( 6x^2 - 20x + 16 \). What a beautiful quadratic! Now let’s not forget the significance of factoring in real-world applications. Quadratics often model projectile motion, such as when throwing a ball, calculating where it will land based on speed and angle. The factors give insights into maximum height (vertex) and intercepts (roots), which can help in sports, engineering, and even video game design! Cool, right?