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Simplifying expressions is a fundamental skill in prealgebra. It helps us make complex problems easier to handle. Let's break down the concept of simplifying expressions step by step.

In the exercise, you start with the equation: \text{\(16 - 3(y + 8)\)}.
The goal is to combine all like terms and reduce the expression to its simplest form. To do this, we often use a few key techniques. One of these is the distributive property, which we'll dive into shortly.

By applying these methods, we turn a more complex expression into something simpler. This can make solving equations easier and help us understand mathematical relationships better.

Combining like terms is a critical component of simplifying expressions. Like terms are terms in an expression that have the same variable raised to the same power. In our example, once we apply the distributive property in \(16 - 3(y + 8)\), we end up with: \text{16 - 3y - 24}.

Here, the numbers 16 and -24 are like terms because they are both constants without variables. Combining them gives us: -8. So, the new expression becomes -8 - 3y.

Why is this important? Combining like terms helps in reducing an expression to its simplest form, making it easier to understand and work with. It lets us easily see the relationship between different parts of an expression, which is especially useful when solving equations or performing further mathematical operations.

Prealgebra is the foundation of all higher-level mathematics. It introduces concepts like the distributive property and combining like terms which are fundamental for algebra and beyond. Understanding these basics is crucial for any student aiming to advance in math.

In our exercise, we started with the expression \(16 - 3(y + 8)\) and simplified it step by step using prealgebra skills. First, by applying the distributive property, and then by combining like terms, we turned it into a simpler expression, \(-8 - 3y\).

These skills build the groundwork for more complex topics in algebra, calculus, and other advanced fields. Knowing how to break down, simplify, and recombine expressions is indispensable for understanding and solving mathematical problems effectively.