(d) \( 2 x+x y-x^{2} \)

Let's break it down in a fun way! This expression \( 2x + xy - x^2 \) is a polynomial in two variables, \( x \) and \( y \). If you picture it as a recipe, \( 2x \) is like the base of your dish, \( xy \) adds a delicious twist with a bit of interaction between \( x \) and \( y \), and \( -x^2 \) is that unexpected sour note that balances the flavor. When you’re simplifying or factoring such expressions, think of combining like terms or searching for common factors, like hunting for hidden treasures! Now, speaking of real-world applications, this expression can represent various scenarios, such as profit calculations in a business where \( x \) is a quantity of products sold, and \( y \) could be the price per item. So, if you're an entrepreneur, mastering these polynomials could help you optimize your profits or analyze trends in sales, giving you the tools to navigate the exciting world of business!