5. \( 4 p^{3}-2 p-p q^{2}+q \) 6. \( 6 m^{2}-2 m n-3 m p+n p \)

Did you know that polynomial expressions, like the ones you provided, are foundational in algebra and help in modeling real-world situations, from calculating areas to predicting trends? When you break them down, each term can represent different aspects, such as varying costs in a business model or growth rates in biology. A common mistake when simplifying polynomials is forgetting to collect like terms. Each term must match in variables and exponents to be combined correctly. Also, watch out for signs; they can easily lead to errors in your final answer. Always double-check your work and simplify step by step!