/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 Identify the terms, like terms, ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 18

Identify the terms, like terms, coefficients, and constants in each expression. \(6 m-2 n+7\)

Short Answer

Expert verified
Terms: \(6m\), \(-2n\), \(7\); Like terms: None; Coefficients: \(6, -2\); Constant: \(7\).

Step by step solution

01

Identify the Terms

To identify the terms in the expression, we need to locate the parts separated by plus or minus signs. The given expression is \(6m - 2n + 7\). This expression has three terms: \(6m\), \(-2n\), and \(7\).
02

Identify Like Terms

Like terms are terms that have the same variable raised to the same power. In this expression, \(6m\) and \(-2n\) are not like terms because they have different variables. The number \(7\) is a constant and doesn't have any like terms with the variables present.
03

Identify the Coefficients

Coefficients are the numerical parts of terms that contain variables. In the expression, the term \(6m\) has a coefficient of \(6\), and the term \(-2n\) has a coefficient of \(-2\). These numbers indicate how many times the variable is multiplied.
04

Identify the Constants

Constants are terms that do not contain any variables and are plain numbers. In this expression, \(7\) is the constant term as it is not attached to any variable.

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.

Terms in Algebra
Algebraic expressions are made up of individual elements known as terms. A term can be a number, a variable, or a combination of both multiplied together. In the case of the expression \(6m - 2n + 7\), terms are the distinct parts divided by the plus or minus signs. This helps us separate our expression into easier-to-manage pieces.

The terms in our example are:
  • \(6m\)
  • \(-2n\)
  • \(+7\)
Each piece plays a unique role in forming the complete expression.
Like Terms
When working with algebraic expressions, identifying like terms is crucial. Like terms have the same variable components raised to the same power. This allows us to combine them more easily during calculations.

In the expression \(6m - 2n + 7\), due to the different variables of \(m\) and \(n\), there are no like terms with each other. Additionally, the constant \(7\) cannot pair with any term because it lacks a variable component. Here鈥檚 what you need to remember about like terms:
  • Must have the same variable.
  • Variables must be raised to the same power.
  • Only like terms can be combined in simplifying expressions.
Coefficients
Coefficients are the numerical parts found in terms with variables. Understanding coefficients is key because they indicate how much of the variable is included in the expression. For example, they tell us how many times the variable should be considered.

In \(6m - 2n + 7\):
  • The coefficient of \(6m\) is \(6\).
  • The coefficient of \(-2n\) is \(-2\).
These numbers determine the impact of the variables within the whole expression.
Constants in Expressions
Constants are the fixed values within an algebraic expression. Unlike terms containing variables, constants maintain the same value across different scenarios and calculations.

In the expression \(6m - 2n + 7\),
  • \(7\) is the constant term.
A constant doesn't fluctuate with the change in variable values, holding its ground as an unchanging number.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

A rectangle has width \(w .\) Its length is one less than twice its width. Write an expression in simplest form for its perimeter.

Find each product mentally. Example $$\begin{aligned}15 \cdot 12 &=15(10+2) \\\&=150+30 \text { or } 180\end{aligned}$$. $$7 \cdot 14$$

Evaluate \(\frac{-4 y}{x}\) if \(x=2\) and \(y=-3\).

An airplane flying at 500 miles per hour leaves Minneapolis. One-half hour later, a second airplane leaves Minneapolis flying in the same direction at a rate of 600 miles per hour. How long will it take the second airplane to overtake the first?

What is the value of \(\frac{3(4 a-3 b)}{b-4}\) if \(a=6\) and \(b=7 ?\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.