/*! 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 74 Perform the operations. $$-2 a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 74

Perform the operations. $$-2 a b+7 a b-3 a b$$

Short Answer

Expert verified
The simplified expression is \(2 a b\).

Step by step solution

01

Identify Like Terms

In the algebraic expression \(-2 a b + 7 a b - 3 a b\), all the terms \( -2 a b, 7 a b, -3 a b\) are like terms because they all have the same variable part \(a b\).
02

Combine Like Terms

The law of combining like terms can directly be applied. The coefficient of each term just needs to be added or subtracted according to its sign. So, the expression becomes \(-2 + 7 - 3) \cdot a b\).
03

Calculate the Coefficient

Calculating the brackets results in \(2 \cdot a b\). This gives us the final simplified expression.

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.

Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. They are a way to express relationships between different quantities. In the expression \(-2ab + 7ab - 3ab\), there are two components: coefficients and variables. The variables here are \(a\) and \(b\), which are being multiplied together in each term. Each term in an expression is separated by a plus (+) or minus (鈭�) sign. These terms could be numbers (constants) or combinations of numbers and variables (like \(-2ab\)).Understanding algebraic expressions is essential for learning how to manipulate and simplify them, which is a key skill in algebra.
Coefficients
Coefficients are the numbers in front of the variables in an algebraic expression. They indicate how many times that term is being added or subtracted. In our expression \(-2ab + 7ab - 3ab\), - \(-2\),- \(7\), - and \(-3\) are the coefficients. These coefficients tell us how much of the variable part \(ab\) is present in each term. When combining terms, you are essentially adding or subtracting these coefficients while retaining the variable part unless the variable is eliminated entirely. It's crucial to handle the signs correctly, as they determine the actual size of the coefficients.
Simplification
Simplification is the process of reducing an expression to its simplest form. Owing to this, we perform operations and combine terms where possible. For the expression \(-2ab + 7ab - 3ab\), the terms are similar because they share the same variable part: \(ab\). To simplify the expression, focus on the coefficients:
  • Add \(7 - 2\) to get \(5\)
  • Then subtract \(3\) from \(5\) to get \(2\)
So now, we have \(2ab\).The main goal of simplification in algebra is to make expressions as simple and manageable as possible, preserving their value. By learning how to simplify, you'll find you're able to solve equations and understand expressions much more easily.

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

Give an example of a polynomial that is \(\ldots\) of degree 1

Graph the function \(f(x)=-x^{2} .\) What do you discover?

The radius of one millstone in the illustration is 3 meters greater than the radius of the other, and their areas differ by \(15 \pi\) square meters. Find the radius of the larger millstone.

How do you add like terms?

The number of feet that a car travels before stopping depends on the driver's reaction time and the braking distance. For one driver, the stopping distance \(d\) is given by the function \(d=f(v)=0.04 v^{2}+0.9 v,\) where \(v\) is the velocity of the car. Find the stopping distance when the driver is traveling at \(30 \mathrm{mph}\).
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics 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.