Final answer:
The question asks to simplify algebraic expressions, demonstrating knowledge in distributing, combining like terms, and applying sign rules in mathematics. The subject deals with fundamental algebraic operations appropriate for middle school grade levels.
Step-by-step explanation:
The student's question revolves around the simplification of various algebraic expressions, which is a fundamental concept in mathematics. Each expression has variables such as y, a, x, m, and r, and includes a series of operations that need to be properly simplified. The goal is to demonstrate how to expand and combine like terms correctly to arrive at a simplified form of each expression.
For example, in the first expression 3(2y + 1) + 4, we distribute the 3 across the terms inside the parentheses to get 6y + 3, and then add the 4, ending up with 6y + 7. Similarly, when we have multiplication of numbers with opposite signs, as in the fourth expression -2(4m + 1) - m, we apply the rules that multiplying two numbers with opposite signs gives a product with a negative sign. Thus, we get -8m - 2 - m, which further simplifies to -9m - 2, combining the m terms.