/*! 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 80 Simplify by combining like terms... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 80

Simplify by combining like terms. $$-j^{3}-j^{3}$$

Short Answer

Expert verified
Question: Simplify the expression $$-j^{3}-j^{3}$$. Answer: $$-2j^{3}$$

Step by step solution

01

Identify the like terms

Notice that both terms in the expression are like terms since they have the same power 3 of the variable j: $$-j^{3}$$ and $$-j^{3}$$.
02

Combine the coefficients of the like terms

To combine like terms, add their coefficients: since the coefficients of both terms are -1, we have $$-1 - 1 = -2$$.
03

Write the simplified expression

Now, we can write the simplified expression by multiplying the combined coefficient with the common variable and its power: $$-2j^{3}$$. The simplified expression is $$-2j^{3}$$.

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.

Simplifying Algebraic Expressions
Simplifying algebraic expressions is like finding the shortest path to reach a destination in a maze.
You start by grouping terms that can be combined, known as like terms. This process helps make expressions more manageable and easier to work with.

Here's how it works:
  • Identify terms with the same variable and exponent. These are your like terms. In our example, \(-j^3\) and \(-j^3\) are like terms because they both have \(j^3\).
  • Once identified, combine these like terms by adding or subtracting their coefficients. This process is what we call simplifying.
  • Finally, rewrite the expression with the simplified terms.
The key is to focus on gathering similar pieces, much like sorting socks from your laundry.
Coefficients in Algebra
In algebra, coefficients play the role of the numbers in charge.
They tell you how many of each variable you have. Understanding coefficients is crucial because they determine the scale of each term within an expression.

Consider this:
  • Coefficients are the numbers directly in front of variables. In \(-j^3\), the coefficient is \(-1\).
  • When combining like terms, add or subtract their coefficients. For \(-j^3 - j^3\), you calculate \(-1 - 1 = -2\).
  • This combined coefficient is then multiplied by the variable and its power, completing the simplified expression.
Coefficients provide a sense of scale and quantity to variables, acting as their numerical guides.
Polynomials
Polynomials are like the multi-storied buildings of algebra.
They're made up of terms, each consisting of a coefficient, a variable, and an exponent.

Understanding polynomials involves:
  • Recognizing each term within the polynomial structure. These terms could be constants, variables, or a mix of both.
  • Identifying like terms within the polynomial to simplify it effectively. In our example, \(-j^3\) and \(-j^3\) are not just terms but parts of a polynomial.
  • Combining these like terms to streamline the polynomial and make calculations more straightforward.
Polynomials form the backbone of many algebraic operations, and mastering them is key to proficiency in algebra.

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

Find the GCF using prime factorization. \(60,120,\) and 140

What is the formula for the surface area of a box? A cube that is 5 centimeters along each side is to be covered with paper. What is the total area that will be covered by the paper?

Find the GCF by listing. 40 and 32

State the conjugate of each binomial. $$y+2$$

Devon paints portraits in three sizes: small, medium, and large. He receives 50 dollar for a small, 75 dollar for a medium, and 100 dollar for a large portrait. It costs him 22 dollar for each small, 33 dollar for each medium, and 47 dollar for each large portrait. a. Write a polynomial that describes the revenue he receives from the sale of all three sizes of portraits. b. Write a polynomial that describes his cost for all three sizes. c. Write an expression in simplest form for his net. d. In one month, he sells 4 small, 6 medium, and 2 large portraits. Find his net profit or loss.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.