2) \( 9(x+1)-3(x+1)^{2} \)

To solve the expression \( 9(x+1)-3(x+1)^{2} \), we can first factor out \( (x+1) \): \[ 9(x+1) - 3(x+1)^{2} = (x+1)(9 - 3(x+1)). \] Next, simplify inside the parentheses: \[ 9 - 3(x+1) = 9 - 3x - 3 = 6 - 3x. \] So, the expression can be rewritten as: \[ (x+1)(6 - 3x). \] Now, this gives us the factored form of the expression: \[ 3(x+1)(2-x). \] This can be a fun puzzle to explore further! We're essentially transforming one expression into another, verifying that both forms are equivalent while also getting creative with our factoring skills. For a practical application, anytime you need to simplify expressions or solve equations in algebra, recognizing patterns like factoring can save time! This skill comes in handy in fields like engineering and programming, where solving for an unknown is often necessary. Keep practicing, and you'll discover how fluid these transformations can become!