/*! 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 42 Identify each group of terms as ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 42

Identify each group of terms as like or unlike. \(t, s\)

Short Answer

Expert verified
The terms \(t\) and \(s\) are unlike terms.

Step by step solution

01

Understand the Definition

Terms are considered 'like terms' if they have the same variable raised to the same power. If they do not share these characteristics, then they are 'unlike terms.'
02

Analyze the Given Terms

Examine the terms: \(t\) and \(s\). Identify the variables and their exponents in each term.
03

Compare the Terms

The first term has the variable \(t\), while the second term has the variable \(s\). Since the variables are different, these terms do not share the same variable raised to the same power.
04

Conclusion

Based on the comparison, the terms \(t\) and \(s\) are 'unlike terms' because they contain different variables.

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.

Algebra Terms
In algebra, terms are fundamental building blocks. A term is a single mathematical expression. It can be a number (also known as a constant), a variable, or numbers and variables multiplied together. For instance, in the expression \(3x + 4y - 7\), \(3x\), \(4y\), and \(-7\) are all terms. Terms can be combined using addition or subtraction.
Variable Comparison
Variables are symbols, usually letters, used to represent unknown values in mathematical expressions and equations. When comparing algebraic terms, we look at the variables and their exponents. For example, in comparing \(3x^2\) and \(5x^2\), both terms have the same variable \(x\) raised to the same power \(2\). This makes them like terms. On the other hand, if we compare \(3x^2\) with \(-4y^3\), the variables and their exponents are different, so these are unlike terms. Clearly distinguishing variables is crucial for solving algebra problems. Make sure they match in both letter and exponent when identifying like terms.
Same Power
Identifying whether terms have the same power is another key step in determining like terms. A power is the exponent indicating how many times the variable is multiplied by itself. For instance, in \(x^3\), the exponent is \(3\), meaning \(x \cdot x \cdot x\). When comparing terms, if the variables are raised to different powers, they are unlike terms. For example, \(x^2\) and \(x^3\) look similar but have different exponents. Therefore, they are unlike terms. Remember, for terms to be like, both the variable and the power must be identical.

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

Solve each problem. In \(2006,\) bachelor's degree recipients from private four-year institutions had an average of \(\$ 18,800\) in total student debt. This average increased \(\$ 1400\) by 2011 and then dropped \(\$ 300\) by \(2016 .\) What was the average amount of total student debt in \(2016 ?\) (Data from The College Board.)

Solve each problem. Marcial owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40\), and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400\). He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \((2 x+y)(3 a)\)

Twice the product of -1 and \(6,\) subtracted from -4

Write a numerical expression for each phrase, and simplify the expression. The sum of 9 and \(-4,\) decreased by 7
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure 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.