/*! 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 41 Simplify each expression. $$-4... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 41

Simplify each expression. $$-4(-p)(-q)$$

Short Answer

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

Step by step solution

01

Simplify the Expression by Removing Parentheses

The expression to be simplified is \[ -4(-p)(-q) \]Get rid of the parentheses by multiplying the terms together. First, multiply the innermost terms: \[ (-p)(-q) = pq \] This is because multiplying two negative numbers results in a positive number.
02

Combine the Terms

Now that we have simplified the innermost terms, the expression looks like this:\[ -4(pq) \]Multiply \(-4\) by \(pq\) to simplify further:\[ -4 \times pq = -4pq \]Thus, the expression is simplified to \[ -4pq \].

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.

Simplification
Simplification in algebra is all about reducing an algebraic expression to its simplest form. This involves combining like terms and eliminating unnecessary parentheses. A great first step is to focus on operations inside parentheses.
  • The exercise in question starts with an expression \[ -4(-p)(-q) \].
  • In this expression, simplifying involves multiplying the terms together to eliminate the parentheses.
  • The first action is working with the innermost part of the expression: multiply \((-p)(-q) = pq\).
  • Once the parentheses are removed, the expression becomes \(-4(pq)\).
The last part of simplification is combining any remaining numbers and variables, which in this case is multiplying \(-4\) with \(pq\), giving the final simplified form \(-4pq\).
Remember, the goal of simplification is to ease solving or further manipulations in an algebraic context.
Multiplication of Integers
Multiplying integers is a basic yet crucial skill in algebra. Here, we deal with whole numbers that could be positive or negative. Let鈥檚 focus on the steps that simplify our expression: -4(-p)(-q).
  • Begin with multiplying two variables with negative signs, \((-p)\) and \((-q)\). The rule is: a negative number times a negative number equals a positive number, thus \((-p)(-q) = pq\).
  • Then, multiply the result with \(-4\). Now, this follows another basic rule: a negative number times a positive number results in a negative number. This calculation gives us \(-4 \times pq = -4pq\).
By systematically following these rules, you transform complex expressions into simpler forms, making them easier to understand and use in further calculations or equations.
Negative Numbers
The concept of negative numbers can be tricky but is very important in algebra. Negative numbers are numbers less than zero, and they play a key role in these operations.
  • When two negative numbers are multiplied, the result is positive. This is because the negative signs cancel each other out (like in our steps where \((-p)(-q)\) becomes \(pq\)).
  • On the other hand, multiplying a negative number with a positive number yields a negative result. For instance, in \\(-4 \times pq = -4pq\), the \(-4\) indicates this rule as it keeps the result negative.
Understanding these signs helps you handle algebraic operations better and predicts the nature (positive or negative) of the results you get from these multiplications.

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

In the newspaper, Ruben read that the low temperature for the day was expected to be \(-5^{\circ} \mathrm{F}\) and the high temperature was expected to be \(8^{\circ} \mathrm{F}\). What was the difference in the expected high and low temperatures?

Evaluate each expression if \(a=0, b=3,\) and \(c=-4\) $$a b+|-40|$$

Find the solution of each equation from the list given. (lesson \(1-5\) ) $$7 a=49 ; 7,42,343$$

Find each quotient. $$91 \div 7$$

Evaluate each expression if \(a=0, b=3,\) and \(c=-4\) $$|c|-b$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.