13) \( 6 x^{2}+4 x y-12 y^{2} \)

Did you know that the expression \( 6x^2 + 4xy - 12y^2 \) can be factored into a more manageable form? By looking for common factors and employing methods like grouping or using the quadratic formula, you can write it as \( 2(3x^2 + 2xy - 6y^2) \). This not only makes calculations easier but can also provide insight into the values of \( x \) and \( y \) that satisfy the equation! In real-world applications, expressions like this can represent various scenarios, ranging from physics problems involving projectile motion to economic models analyzing profit and loss. Understanding how to manipulate and factor these expressions is crucial, as it often unveils hidden relationships between variables, making it easier to model and predict real-life scenarios!