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Chapter 1: Problem 8

Simplify each expression. $$ 8+3(s-6 t) $$

Short Answer

Expert verified
8 + 3s - 18t

Step by step solution

01

- Distribute the 3

Apply the distributive property by multiplying 3 with each term inside the parentheses: i.e., 3(s - 6t) = 3s - 18t.
02

- Rewrite the expression

Replace the original expression with the result from Step 1: \(8 + 3(s - 6t)\) becomes \(8 + 3s - 18t\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property
The distributive property is an essential algebraic rule. To apply it, you multiply a single term by each term inside a set of parentheses. Consider the expression: \(3(s - 6t)\). Here, the distributive property means you multiply 3 by both \(s\) and by \(-6t\). Doing this gives you \(3s\) and \(3 \times -6t\), which simplifies to \(3s - 18t\). Hence, distributed, it becomes: \(3(s - 6t) = 3s - 18t\). Always ensure you multiply each term correctly, considering the signs (+/-).
Algebraic Simplification
After using the distributive property, the next step is algebraic simplification. Algebraic simplification involves rewriting expressions in a simpler form to make them easier to work with. In our example, once we distribute the 3 through the parentheses, we rewrite \(8 + 3(s - 6t)\) as \(8 + 3s - 18t\). This means our complex expression has been broken down into simpler components which can be further managed or understood. Simplification often makes subsequent steps in problem-solving more straightforward.
Like Terms
In algebra, 'like terms' refer to terms that have the same variable raised to the same power. Identifying like terms allows you to combine them, further simplifying expressions. For instance, in \(8 + 3s - 18t\), the terms \(3s\) and \(-18t\) are unlike terms because they contain different variables. Similarly, 8 is a constant term and is not combined with the others. Recognizing like terms is crucial in algebra because it ensures accuracy in combining terms during simplification. Always double-check. Terms must be identical in variable and exponent to be combined.

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