/*! 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 25 Simplify expression. \(4+2 m+m... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 25

Simplify expression. \(4+2 m+m\)

Short Answer

Expert verified
The simplified expression is \(3m + 4\).

Step by step solution

01

Identify Like Terms

In the expression given, take a look at the terms and identify those that are like terms. In this case, both terms containing the variable 'm', namely '2m' and 'm', are like terms. The constant term '4' is a standalone term.
02

Combine Like Terms

Combine these identified like terms by adding their coefficients. The coefficients for the like terms '2m' and 'm' are 2 and 1, respectively. Thus, the sum is: \(2m + m = 3m\).
03

Write the Simplified Expression

Once the like terms are combined, rewrite the expression by placing the resultant term next to any constant terms. Thus, the simplified expression is \(3m + 4\).

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.

Understanding Like Terms
In the world of algebra, like terms are terms that contain the same variable raised to the same power. Understanding like terms is crucial when simplifying expressions. For example, in the expression \(4 + 2m + m\), both \(2m\) and \(m\) contain the variable 'm' and are therefore like terms. The term \(4\), however, does not have any variables attached, making it a constant term and not similar to the others. Identifying like terms is the first step in simplifying expressions because they are the terms that we can directly combine through addition or subtraction.

To quickly spot like terms, look for terms that:
  • Have the same variable(s).
  • Have the same exponent(s) on these variables.
The Art of Combining Like Terms
Once you've identified like terms in an expression, the next task is to combine them. This is a straightforward process that involves adding or subtracting the coefficients, which are the numerical parts of the terms. The variable part of the terms does not change. Consider the coefficients of \(2m\) and \(m\), which are 2 and 1 respectively.

By adding these coefficients together, \(2 + 1\), we end up with \(3m\). Essentially, combining like terms helps condense an expression, making it more manageable and easier to work with.

Remember:
  • Combine terms with the same variable by adding or subtracting their coefficients.
  • Keep the variable part unchanged.
Mastering Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and operation symbols. Simplifying these expressions by combining like terms is an essential skill in algebra that helps you solve equations and perform calculations more efficiently. For our example, \(4 + 2m + m\), we have:
  • The term '4', which is a constant.
  • Like terms '2m' and 'm'.
The final step in simplifying is to rewrite the expression as \(3m + 4\), where the like terms have been combined and the constant is added for completeness.

As you become more adept at spotting and combining like terms, working with algebraic expressions will become second nature. Always:
  • Start by identifying like terms within the expression.
  • Combine them to simplify the expression.
  • Rewrite the expression to clearly display the simplified form.

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

Use the Distributive Property to write each expression as an equivalent algebraic expression. $$(x-3) 12$$

A ticket to a baseball game costs \(t\) dollars. A soft drink costs \(s\) dollars. Which expression represents the total cost of a ticket and soft drink for \(p\) people? A. \(p s t\) C. \(t(p+s)\) B. \(p+(t s)\) D. \(p(t+s)\)

Explain why formulas are important in math and science. Include an example of a formula from math or science that you have used and an explanation of how you used the formula.

Use the Distributive Property to write each expression as an equivalent algebraic expression. $$15(s-3)$$

Find sum. \(10+(-1)\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

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.