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Algebraic expressions are essentially mathematical phrases that can include numbers, variables, and operation signs. They do not have an equals sign like an equation and are used to represent relationships between variables and constants. A variable is a symbol, often a letter such as 'm', 'u', or 't', that represents an unknown or varying amount. Constants are specific numbers. Operations can include addition, subtraction, multiplication, division, and more.

Consider the exercise you're working on: you're asked to translate a verbal statement into an algebraic expression. This is a common task in algebra, which serves as the foundational language of mathematics. The statement involves a difference, which indicates subtraction, and a product, suggesting multiplication. By identifying operations and corresponding numbers and variables, you move towards constructing a meaningful algebraic expression. This particular skill is handy when approaching calculus, physics, financial math, and many other advanced topics where algebra is employed to model real-world problems.

While algebraic expressions can contain variables, numerical expressions are made up entirely of numbers and operations without any variables. For instance, the expression '5 + 3' is a numerical expression since it only contains numbers and an addition sign.

To grasp numerical expressions, think about operations as instructions. For example, '6 divided by 3' tells you to take the number six and divide it by three, resulting in two. In the textbook exercise, squaring a number and finding products are operations that can be done numerically if values for the variables were provided. Understanding how to evaluate numerical expressions comes in handy when you want to simplify parts of an algebraic expression or when checking specific cases by substiting in values for the variables.

Squaring a number means multiplying that number by itself. The term 'square' comes from the geometric shape of the same name, where all sides are of equal length. When you square a number, you are essentially calculating the area of a square with sides of that length.

Mathematically, squaring is represented by the exponent 2. For example, to square the number 3, you do the following operation: \(3^2 = 3 * 3 = 9\). The square of a negative number is always positive, because multiplying two negative numbers gives a positive result—so, squaring -3 also yields 9. Squaring can also extend to variables, as seen in the expression from the exercise, where 'm' is squared. Understanding the squaring of numbers is vital when you encounter quadratic expressions, power functions, and many other mathematical concepts where exponents play a key role.