f. \( 5 x^{2}+3 x^{2} y \)

Did you know that polynomials, like the one you’re working with, have been around since ancient civilizations? The Egyptians and Babylonians used early forms of algebraic expressions to solve practical problems like land measurement and trade. Today, polynomials serve as the backbone of many scientific fields, from physics to economics, helping to model and solve complex systems! When simplifying polynomials like \( 5x^{2} + 3x^{2}y \), remember to identify and combine like terms carefully. In this case, \( 5x^{2} \) is already a standalone term, while \( 3x^{2}y \) is a distinct term with a different variable part. Avoid common mistakes, such as trying to combine them without factoring them out; they can't be simplified further together!