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Chapter 1: Problem 40

Simplify each expression. $$ -4 z-8 z $$

Short Answer

Expert verified
-12z

Step by step solution

01

Identify Like Terms

The given expression is \(-4z - 8z\).Both terms involve the variable \(z\) and can be combined because they are like terms.
02

Combine Like Terms

To simplify the expression, add the coefficients of the like terms together:\(-4z - 8z = (-4 - 8)z\).
03

Perform the Arithmetic Operation

Calculate the sum of the coefficients:\(-4 - 8 = -12\). Thus, the simplified expression is:\(-12z\).

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Key Concepts

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

like terms
When working with algebraic expressions, it's vital to recognize and combine like terms. Like terms are terms that have the same variables raised to the same power. In the exercise, the terms \(-4z\) and \(-8z\) are like terms because they both contain the variable \z\. Identifying like terms simplifies the process of combining them, which is essential in reducing expressions. For example, in the expression \(-4z - 8z\), both terms are like terms because they share the variable \z\. This allows the coefficients (the numerical part of the terms) to be combined.
coefficients
Coefficients are the numerical part of the terms that are multiplied by the variables. In the given expression \(-4z - 8z\), the numbers \(-4\) and \(-8\) are coefficients. These coefficients represent how many times the variable \z\ will be added or subtracted. To combine like terms, simply add or subtract their coefficients. For instance, in the step \(-4z - 8z = (-4 - 8)z\), we are adding the coefficients \(-4\) and \(-8\) to get \(-12\). Thus, the expression becomes \(-12z\). Always combine coefficients to simplify the expression effectively.
arithmetic operations
Arithmetic operations, like addition, subtraction, multiplication, and division, are fundamental in simplifying algebraic expressions. In our exercise, subtraction is used to combine the coefficients of the like terms. After identifying like terms and their coefficients, perform the arithmetic operation to combine them. For \(-4z - 8z\), subtract the coefficients: \(-4 - 8\). This arithmetic operation yields \(-12\). So, the simplified expression is \(-12z\). Remember to carefully perform arithmetic operations to ensure the correct simplification of expressions.

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