S1 \( (3 x-1)(2 x+3) \)

To solve the expression \( (3x - 1)(2x + 3) \), you can use the distributive property, often referred to as the FOIL method for binomials. Multiplying gives us \( 3x \cdot 2x + 3x \cdot 3 - 1 \cdot 2x - 1 \cdot 3 \). This simplifies to \( 6x^2 + 9x - 2x - 3 \), which further combines to \( 6x^2 + 7x - 3 \). Voilà! You have a quadratic expression ready to rock! In algebra, learning how to correctly expand expressions lays the foundation for many advanced topics, like factoring or solving quadratic equations. Mastering these skills can help boost confidence and make tackling calculus and beyond a whole lot easier. Plus, who doesn't love to impress their friends by solving complex math problems? Time to shine!