Final answer:
The student's question seems to involve algebra, particularly working with expressions and equations by simplifying and factoring. Main concepts include combining like terms and recognizing factors within polynomial expressions. A step-by-step approach is needed to solve specific problems, which are not fully detailed in the question.
Step-by-step explanation:
The question from the student involves the subjects of algebra, expressions, and equations. Without specific values or more context, a generalized approach to the given expressions and equations can be provided. For example, the expression “(-5xyz +2xy² ) + 9xy² -8xy)” involves combining like terms and simplifying the polynomial. In this case, you would combine the terms involving xy². The term “-8p²q²” is described as a factor, which indicates that it is an element of a multiplication operation within an algebraic expression or equation.
For simplification of such expressions: Combine like terms by adding or subtracting coefficients and keeping the variables the same. To factor an expression like “-8p²q²”, we look for common factors in each term, which would typically be p, q, or numbers that can divide the coefficient without a remainder.
The scattered references to other mathematical concepts such as vectors, integrals, and powers of numbers cannot be directly addressed without more context. However, they suggest topics related to vector mathematics, calculus, and exponential rules, which are advanced mathematical topics commonly discussed in high school and college math courses. To appropriately assist with any of these, more information or a specific question is required.