/*! 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 54 Simplify. $$(-3 b)(-4)$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 54

Simplify. $$(-3 b)(-4)$$

Short Answer

Expert verified
The simplified form of \((-3 b)(-4)\) is \(12b\).

Step by step solution

01

Apply multiplication rule

The product of two negative numbers is a positive number, so the product of (-3b) and (-4) becomes +12b. Therefore, the simplified form of \((-3 b)(-4)\) is \(12b\).

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.

Negative Numbers Multiplication
Multiplication of negative numbers can often seem confusing. Yet, it's just an extension of regular multiplication but with a twist. Here is how it works:
  • When you multiply two negative numbers, their product is always a positive number. This is because a negative times a negative cancels out the negative sign.
  • The basic logic is derived from the number line. Where moving left is considered negative and moving twice to the left cancels the direction, bringing it back to positive.
For example, in the expression \((-3 b)(-4)\), both \(-3b\) and \(-4\) are negative, resulting in a positive \(12b\) after multiplication. This underscores the rule that negatives cancel each other out when multiplied.
Positive and Negative Rules
Positive and negative rules in mathematics are essential for simplifying expressions, especially in algebra.
  • When a positive number is multiplied by a negative number, the result is always negative.
  • Conversely, when a negative number is multiplied by another negative number, the result becomes positive.
  • This aspect of arithmetic represents the inherent symmetry on the number line.
In our example: \((-3 b)(-4)\), applying the rule of multiplication for negative numbers, results in a positive \(12b\). Recognizing these rules simplifies solving algebraic expressions efficiently.
Basic Algebra
Basic Algebra involves using symbols and letters to represent numbers and quantities in formulas and equations. This fundamental aspect of mathematics allows us to simplify and solve complex problems with ease.
In our focus example, \((-3 b)(-4)\), algebraic terms can be multiplied by applying the rules of arithmetic concerning signs.
  • Algebraic expressions may involve constants, variables, and operational symbols such as addition, subtraction, multiplication, and division.
  • The symbol \(b\) represents a variable whose value may change based on context or additional equations.
Understanding these elements helps in breaking down expressions and computations into understandable steps.
Introductory Algebra Concepts
When you first encounter algebra, it can seem daunting. However, introductory concepts aim to break down these complexities. Here are some concepts to help you understand the basics:
  • Variables: Symbols (like \(b\)) used to represent unknown values.
  • Expressions: Combinations of numbers, variables, and operations that represent a value.
  • Simplification: The process of reducing an expression to its most basic form.
In our context, the expression \((-3 b)(-4)\) is simplified to \(12b\) by recognizing that the signs affect the outcome and applying multiplication straightforwardly. By grasping these concepts, you'll ease through algebra with confidence and efficiency.

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

Simplify. $$-\left(3 a^{2}+5 a-4\right)$$

Simplify. $$-3\left(-4 x^{2}+3 x-4\right)$$

Simplify. $$-5(3 y-7)$$

Translate into a variable expression. Then simplify. five more than the sum of a number and six

Use the following situation: 83 more students enrolled in spring-term science classes than enrolled in fall-term science classes. If \(n\) and \(n-83\) represent the quantities in this situation, what is \(n ?\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision 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.