/*! 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 44 Remove parentheses and simplify ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 44

Remove parentheses and simplify each expression. $$ (8-5 y)-(4+3 y) $$

Short Answer

Expert verified
The simplified expression is \(4 - 8y\).

Step by step solution

01

Distribute the Negative Sign

The given expression is \((8 - 5y) - (4 + 3y)\). First, we need to distribute the negative sign across the second set of parentheses. This changes the expression to \(8 - 5y - 4 - 3y\).
02

Combine Like Terms

Now that parentheses have been removed, we'll combine like terms. Start with the constant terms: \(8 - 4 = 4\). Next, combine the \(y\)-terms: \(-5y - 3y = -8y\).
03

Write the Final Simplified Expression

The simplified expression, combining all like terms, is \(4 - 8y\).

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 Expressions
When working with algebraic expressions, one of the primary goals is to simplify them. Simplifying expressions means to perform operations and combine all possible terms, reducing the expression to its simplest form. Consider the expression \[ (8 - 5y) - (4 + 3y) \]from the original exercise. We needed to simplify it by removing parentheses and combining terms. This process helps in making complicated expressions easier to work with or solve. Simplification involves:
  • Removing parentheses by applying distribution, if necessary.
  • Combining like terms to consolidate the expression.
Ultimately, the simplified expression should contain the fewest terms possible, making further algebraic manipulations much easier.
Like Terms
In algebra, like terms are terms that have identical variable parts. For example, in the expression \( 8 - 5y - 4 - 3y \),the terms \(-5y\)and \(-3y\)are like terms because they both involve the variable \(y\)raised to the same power (which is 1 in this case).Here's how you identify and combine like terms:
  • Look for terms that have the same variable and power. For instance, \(-5y\)can be combined with \(-3y\)because both have \(y\).
  • Constant terms, like \(8\)and \(-4\),are also considered like terms as they don鈥檛 have any variable.
  • You can add or subtract like terms by simply combining their coefficients. So, \(-5y - 3y = -8y\)and \(8 - 4 = 4\).
Combining like terms is crucial in simplifying expressions as it reduces the number of terms to the simplest form.
Distributive Property
The distributive property in algebra is a useful tool that allows you to multiply a single term across terms within parentheses. In the context of the original expression,\[ (8 - 5y) - (4 + 3y) \],we apply this property indirectly by distributing the negative sign. Here's how the distributive property works:
  • Multiply the term outside the parentheses by each term inside. If you have \(-1\) outside, multiply each inside term by \(-1\).
  • For instance, applying in the expression gives us \(-(4 + 3y) = -4 - 3y\).The expression then transforms to \(8 - 5y - 4 - 3y\).
  • This step ensures that all terms are correctly added or subtracted when combining later.
Understanding the distributive property is fundamental for managing expressions, especially when dealing with terms in parentheses. It allows you to extend the expression so you can proceed with combining like terms.

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

Subtract. \(-17-(-17)\)

Insert one set of parentheses so that the following expression simplifies to 32 . $$ 20-4 \cdot 4 \div 2 $$

A commercial jetliner hits an air pocket and drops 250 feet. After climbing 120 feet, it drops another 178 feet. What is its overall vertical change?

Decide whether the given number is a solution of the given equation. \(4=1-x ; 5\)

Translate each phrase to an algebraic expression. Use " \(x\) " to represent "a number." Add a number and -36 .
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Probability and Statistics

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.