/*! 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 140 Combine like terms. $$ 7 m^{... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 140

Combine like terms. $$ 7 m^{5}-2 m^{3}+8 m^{5}-m^{3} $$

Short Answer

Expert verified
15m^5 - 3m^3

Step by step solution

01

Identify like terms

Locate the terms that have the same variable and the same exponent. In this case, the like terms are: \(7m^5\) and \(8m^5\), also \(-2m^3\) and \(-m^3\).
02

Combine the terms with \(m^5\)

Add the coefficients of \(7m^5\) and \(8m^5\). This gives: \(7 + 8 = 15\), so \(7m^5 + 8m^5 = 15m^5\).
03

Combine the terms with \(m^3\)

Add the coefficients of \(-2m^3\) and \(-m^3\). This gives: \(-2 - 1 = -3\), so \(-2m^3 - m^3 = -3m^3\).
04

Write the final expression

Combine the results from the previous steps to get the final expression: \(15m^5 - 3m^3\).

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.

Intermediate Algebra
Intermediate algebra focuses on consolidating the foundational knowledge from basic algebra and extending these concepts further. It often involves working with more complex equations and expressions. One of the critical skills learned in intermediate algebra is the ability to manipulate and simplify polynomial expressions effectively. This includes understanding how to combine like terms, factor expressions, and solve various types of equations. In this exercise, you practiced combining like terms, a fundamental step in simplifying algebraic expressions.
Polynomial Expressions
Polynomial expressions are mathematical expressions involving a sum of powers of variables with numerical coefficients. In simpler terms, they鈥檙e sums of terms that include variables raised to positive integer exponents and their coefficients. For example, expressions like \(7m^5 - 2m^3 + 8m^5 - m^3\) are polynomials. Polynomials can have multiple terms, and when simplifying them, it's essential to combine like terms, which are terms that have the same variable raised to the same power. This exercise required identifying and combining like terms such as \(7m^5\) and \(8m^5\), as well as \(-2m^3\) and \(-m^3\), leading to a simplified polynomial expression.
Simplifying Algebraic Expressions
Simplifying algebraic expressions is one of the cornerstones of algebra. The goal is to rewrite expressions in the simplest and most efficient form. This generally involves combining like terms, factoring, and reducing fractions. In the given problem, simplifying the expression \(7m^5 - 2m^3 + 8m^5 - m^3\) starts with identifying like terms. Terms like \(7m^5\) and \(8m^5\) can be combined because they share the same base and exponent. Likewise, \(-2m^3\) and \(-m^3\) are combined. The process involved:
  • Locating terms with the same variable and exponent.
  • Adding or subtracting the numerical coefficients of these like terms.
  • Writing the simplified expression which, in this case, is \(15m^5 - 3m^3\).
It is essential to be methodical and precise to avoid mistakes and ensure accuracy when simplifying.

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

Express each radical in simplified form. Assume that all variables represent positive real numbers. $$ \sqrt[3]{\frac{y^{17}}{125}} $$

Express each radical in simplified form. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{v^{13}}{49}} $$

Write with rational exponents, and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form. $$ \sqrt[3]{\sqrt[5]{\sqrt{y}}} $$

Simplify by first writing the radicals as radicals with the same index. Then multiply. Assume that all variables represent positive real numbers. $$ \sqrt{x} \cdot \sqrt[3]{x} $$

Perform the indicated operations. Give answers in standard form. $$ \frac{2}{3+4 i}+\frac{4}{1-i} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

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.