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Chapter 1: Problem 361

In the following exercises, simplify using the Distributive Property. $$ -3(x-6) $$

Short Answer

Expert verified
-3x + 18

Step by step solution

01

Identify the Expression

The given expression is \( -3(x-6) \).
02

Apply the Distributive Property

Distribute \( -3 \) to both terms inside the parentheses. The Distributive Property states that \( a(b + c) = ab + ac \). In this case, \( a = -3 \), \( b = x \), and \( c = -6 \). So, \( -3(x) \) and \( -3(-6) \).
03

Perform the Multiplication

Multiply \( -3 \) by each term inside the parentheses: \[ -3 \times x = -3x \] \[ -3 \times -6 = 18 \]
04

Combine the Results

Combine the results from the previous step: \[ -3x + 18 \]

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Key Concepts

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

Simplifying Expressions
Simplifying expressions comes down to making an algebraic phrase more manageable. When simplifying, the aim is to rewrite the expression in its simplest form by using mathematical rules. For example, given the expression \( -3(x-6) \), we have to make it simple and neat.
Applying the Distributive Property helps us to break it down. Notice that simplification might involve distributing, combining like terms, and reducing fractions. This makes the calculation easier and more straightforward to work with.
Algebraic Multiplication
Algebraic multiplication involves multiplying numbers and variables. These multiplications follow specific rules.
For instance, in the expression \( -3(x-6) \), we use the Distributive Property to multiply \-3\ by each term inside the parentheses: First, \( -3 \times x = -3x \) and then \-3 \times -6 = 18\. The result from each multiplication forms part of the simplified expression.
Remember: When multiplying negative numbers, two negatives make a positive. So, \-3 \times -6 \ becomes 18, making the simplified form \(-3x + 18\).
Combining Like Terms
Combining like terms is essential in simplifying algebraic expressions. Like terms are terms with the same variable raised to the same power. Our objective is to add or subtract them to make the expression simpler.
In the provided example, the terms from the distribution \(-3x\ and \18\) are unlike terms. Hence, they cannot be combined further. This results in the final simplified expression: \(-3x + 18\). Combining like terms allows us to consolidate parts of the expression, making it easier to work with in solving equations or evaluating the expression.

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Most popular questions from this chapter

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