(2) \( 9 b^{4}+3 b^{2}-12 b^{6} \)

Let's simplify the expression step by step! You want to combine like terms and factor where possible. First, rearranging the terms gives us \( -12b^6 + 9b^4 + 3b^2 \). Now, factor out the greatest common factor (GCF), which in this case is \( 3b^2 \): \[ 3b^2(-4b^4 + 3b^2 + 1) \] Now, we can focus on the quadratic \( -4b^4 + 3b^2 + 1 \) if needed, but that might be enough for a clean simplification! Happy factoring! Did you know that polynomials like this one can often model real-world phenomena, such as the trajectory of a projectile? By analyzing the coefficients and terms, one can derive insights into the motion of objects under gravity, helping engineers and scientists make predictions and optimize designs. Polynomials are more than just numbers; they're the language of change in many fields! When simplifying polynomials, a common mistake is to overlook the negative signs or to add coefficients incorrectly. Always double-check your arithmetic and factor by grouping if you get stuck. It’s like putting together a puzzle—everything needs to fit just right for the final picture to emerge! Keep a close eye on those signs!