/*! 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 82 Use the distributive property to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 82

Use the distributive property to rewrite each expression. $$ -4(3 x-2) $$

Short Answer

Expert verified
-12x + 8

Step by step solution

01

Recognize the Distributive Property

The distributive property states that for any numbers or expressions, \(a(b + c) = ab + ac\) and \(a(b - c) = ab - ac\). This means you can distribute the multiplication over addition or subtraction inside the parentheses.
02

Apply the Distributive Property

To apply the distributive property, multiply \(-4\) by each term inside the parentheses: \(-4(3x)\) and \(-4(-2)\).
03

Simplify the Expressions

Multiply the constants: \(-4 \times 3x = -12x\). Next, multiply \(-4 \times -2 = 8\). So the expression becomes \(-12x + 8\).

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.

Understanding Algebraic Expressions
Algebraic expressions are a combination of numbers, variables, and operations. A variable represents an unknown value and is usually denoted by a letter like x or y. In the expression -4(3x - 2), -4 is a constant, 3x is a term with a variable, and -2 is also a constant. Learning to manipulate these expressions is essential in algebra. Always remember to follow the order of operations, typically known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Mastering Multiplication in Algebraic Context
Multiplication in algebra involves not just numbers but also variables and expressions. When using the distributive property, you multiply the term outside the parentheses by each term inside the parentheses individually. In the example -4(3x - 2), you have to distribute -4 to both 3x and -2. First, multiply constants with variables: -4 * 3x equals -12x. Then multiply the constants: -4 * -2 equals 8. These steps help simplify complex expressions and make solving equations easier.
Steps to Simplification
Simplification means reducing an expression to its simplest form. Use the distributive property to break down and simplify algebraic expressions. Here鈥檚 a quick recap:
  • Distribute the multiplication across the terms inside the parentheses.
  • Combine like terms if necessary.
  • Ensure all calculations are correct, especially sign changes.
In the exercise -4(3x - 2), applying these steps results in -12x + 8. Simplifying expressions correctly ensures better understanding and easier problem-solving 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

Write a numerical expression for each phrase, and simplify the expression. 14 added to the sum of -19 and -4

Write a numerical expression for each phrase, and simplify the expression. The product of \(-\frac{1}{2}\) and \(\frac{3}{4},\) divided by \(-\frac{2}{3}\)

Use the distributive property to rewrite each expression. $$ -\frac{1}{4}(8 x+3) $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \((-5+x)(-3+y)(3-a)\)

Write a numerical expression for each phrase, and simplify the expression. The sum of \(\frac{3}{4}\) and \(\frac{1}{2},\) times the difference of \(\frac{2}{3}\) and \(\frac{1}{6}\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

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.