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Simplifying expressions is an essential skill in algebra that involves making a mathematical expression more straightforward without changing its value. In this context, the Distributive Property is a crucial tool. This property allows us to deal quickly with expressions that have parentheses, like our initial expression \(8(k+3)\). By using the distributive property, we can break down complex expressions into simpler forms that are easier to work with. To simplify, look for opportunities to apply rules like combining like terms or distributing multiplication over addition, as you did with the expression by multiplying 8 by both \(k\) and 3. Simplifying expressions helps to make problems more manageable and solutions more apparent.

Algebraic multiplication involves the multiplication of numbers, variables, or a combination of both. In your exercise, this occurred when multiplying the constant 8 by each term inside the parentheses \((k+3)\). This technique is part of using the Distributive Property. Here’s how it works:

• Multiply the constant by each term inside the parentheses separately.
• In this example: \(8 \cdot k\) which gives \(8k\), and \(8 \cdot 3\) which gives 24.

This process of algebraic multiplication helps in breaking down complex expressions and simplifies tasks like simplifying or solving equations further down the line.

The expression in your problem assumes all variables are nonnegative real numbers. In mathematics, nonnegative real numbers are numbers that are either positive or zero. This means, any value \(k\) in the expression \(8(k + 3)\) is not lesser than zero. This assumption is critical when simplifying expressions and performing operations on variables because some rules may apply differently if variables can take negative values. Working under the assumption of nonnegative real numbers ensures the expressions and operations like multiplication remain valid and straightforward, without introducing complications like imaginary numbers or dealing with undefined division by zero issues.