Problem 21 Specify each term. $$-6 a-5 b$... [FREE SOLUTION]

Chapter 11: Problem 21

Specify each term. $$-6 a-5 b$$

Short Answer

Expert verified

Terms: $-6a$ and $-5b$.

Step by step solution

Identify Terms

Terms in an algebraic expression are individual components separated by plus (+) or minus (-) signs. Here, the expression is $-6a - 5b$.

Specify Each Term

In the expression $-6a - 5b$, there are two terms. The first term is $-6a$ and the second term is $-5b$. Each term consists of a constant (coefficient) and a variable.

Breakdown of the First Term

The first term $-6a$ consists of a coefficient $-6$ and a variable $a$. This means $-6a$ stands for $-6$ times $a$.

Breakdown of the Second Term

The second term $-5b$ consists of a coefficient $-5$ and a variable $b$. This means $-5b$ stands for $-5$ times $b$.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Coefficients

A coefficient is a number that multiplies a variable within an algebraic term. In the expression $-6a - 5b$, the coefficients are $-6$ and $-5$. The sign of the coefficient indicates whether the term is positive or negative. Here are the main points to remember about coefficients:

They determine the magnitude of the term. For instance, in $-6a$, the coefficient $-6$ shows how many times the variable $a$ is counted.
The coefficient can be positive or negative. If it is negative, as in $-6$, it means that the term is subtracted.
The absence of a written number in a term indicates a coefficient of 1. For example, the term $x$ is essentially $1x$.

Understanding coefficients is crucial because they affect how we perform operations with algebraic expressions. Remember, always combine like terms by their coefficients directly.

Variables

Variables are symbols used to represent unknown or changeable values in algebraic expressions. In the expression $-6a - 5b$, the variables are $a$ and $b$. These symbols stand in for numbers, and here's more about them:

Variables can take various values. Their exact value depends on the context or any given condition.
They are crucial for creating formulas and expressions, allowing flexible usage in different scenarios.
Variables are typically represented by letters such as $x, y, a, b$, etc.

Variables might initially seem abstract, so think of them as placeholders for numbers. They allow you to generalize mathematical situations.

Terms in Algebra

In algebra, a term is a single mathematical expression. It can be a number, a variable, or a combination of numbers and variables, often involving coefficients and powers. Let's look into the expression $-6a - 5b$, which includes two terms: $-6a$ and $-5b$. Here鈥檚 what you should know:

Terms are the building blocks of algebraic expressions. They are separated by plus (+) or minus (鈭�) signs.
Each term consists of a coefficient and a variable factor, possibly raised to an exponent.
The degree of a term is the exponent of the variable. If no exponent is shown, the variable is to the power of one.

Understanding how to identify and work with terms is essential for simplifying expressions and solving equations. Always focus on terms to break down and reorganize algebraic expressions effectively.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Specify each term. $$-6 a-5 b$$

Short Answer

Step by step solution

Identify Terms

Specify Each Term

Breakdown of the First Term

Breakdown of the Second Term

Key Concepts

Coefficients

Variables

Terms in Algebra

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.