b) \( 6 x^{2}+3 x y-2 x t-y t \)

To factor the expression \( 6 x^{2}+3 x y-2 x t-y t \), we can start by grouping terms strategically. Notice that the first two terms can be factored with \( 3x \) as a common factor, giving us \( 3x(2x + y) \). For the last two terms, we can factor out \( -t \), resulting in \( -t(2x + y) \). Now, our expression looks like this: \[ 3x(2x + y) - t(2x + y) \] Now, we can combine the two terms since they share the common factor \( (2x + y) \): \[ (2x + y)(3x - t) \] And voilà! The factored form of the expression is \( (2x + y)(3x - t) \). But wait, there’s more! This factoring technique shows how understanding common factors can simplify seemingly complex expressions. You’re not just playing with numbers; you're solving puzzles that can appear in various real-world contexts, like optimizing functions or dealing with geometric problems. Why not take it a step further and see how these factored forms can help you in calculus, where understanding the structure of polynomials is essential for derivatives and integrals? It’s like having superpowers for tackling math!