/*! 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 72 Use the distributive property to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 72

Use the distributive property to rewrite the expression without parentheses. $$ (3 x+8)(-2) $$

Short Answer

Expert verified
The expression (3x+8)(-2) rewritten without parenthesis using the distributive property is \(-6x - 16\).

Step by step solution

01

Identify the expression to distribute

Firstly, identify that -2 needs to be distributed to both the terms inside the parenthesis that is \(3x\) and \(8\).
02

Apply distributive property

Next step is to apply the distributive property which means multiply -2 with \(3x\) and then multiply -2 with \(8\). So, the expression becomes \(-2*3x + (-2*8)\).
03

Simplify the expression

-2 multiplied with \(3x\) gives \(-6x\) and -2 multiplied with 8 gives -16. So, the expression simplifies to \(-6x - 16\).

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
Simplifying expressions is an essential skill in algebra, as it allows you to rewrite mathematical expressions in their simplest form. This is done by combining like terms and applying mathematical properties, such as the distributive property. When simplifying expressions, you'll want to reduce the number of terms and eliminate any unnecessary parentheses.
  • Identify the algebraic terms: Separate constants from variables, ensuring each term is distinct.
  • Look for opportunities to use mathematical properties: Apply identities like commutative, associative, and distributive properties to break down expressions.
  • Combine like terms: Like terms are terms that have the exact same variable parts (e.g., same variable and exponents). Add or subtract them accordingly.
When working with negative numbers while simplifying, ensure that you carefully follow the rules for adding, subtracting, multiplying, or dividing these numbers.
Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operational symbols like addition and multiplication. They do not have an equality sign, which distinguishes them from equations.
  • Components of algebraic expressions: These include constants, coefficients, variables, and terms.
  • Constants are fixed numbers, whereas coefficients are numbers that multiply a variable.
  • Variables represent unknown values and are usually denoted by letters like x or y.
Understanding how to manipulate these expressions is important because it allows you to model real-world situations and solve problems. The distributive property is crucial in rearranging expressions, especially when parentheses are involved. It simplifies the expression, helping you avoid unnecessary complications.
Negative Numbers
Negative numbers are numbers less than zero, represented with a minus sign (-). They might seem a bit tricky at first, but they're essential in expressing concepts like debt, temperature below zero, or any deficit.
  • Basic rules of operations with negatives:
    • Adding a negative is like subtracting a positive (e.g., 5 + (-3) = 5 - 3).
    • Subtracting a negative number is like adding its opposite positive number (e.g., 5 - (-3) = 5 + 3).
    • Multiplying or dividing two negative numbers gives a positive result, while one negative and one positive yields negative.
  • Think of the number line: Negative numbers go to the left of zero, so they decrease in value compared to positive numbers.
When using the distributive property, dealing with negative numbers requires careful attention to the signs to avoid mistakes in the final expression. Remember, keeping track of negative signs is crucial for correct simplification of expressions.

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

To raise money, your student council is selling magazine subscriptions. The student council will receive a one-time bonus of 150 dollar from the magazine publisher plus 38% of the subscription money. The following verbal model represents the situation. How much subscription money is needed for the council to raise a total of $300? Round your answer to the nearest dollar.

GREATEST COMMON FACTOR Find the greatest common factor of the pair of numbers. (Skills Review p. 761 ) $$ 17,51 $$

GREATEST COMMON FACTOR Find the greatest common factor of the pair of numbers. (Skills Review p. 761 ) $$ 27,36 $$

Solve the equation. $$ 5(-x+2)=-3(7 x+2)+8 x $$

Solve the percent problem. 18 is 25% of what number?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

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.