/*! 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 18 Multiply. $$ -6(5 x 2+2 x-1)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 18

Multiply. $$ -6(5 x 2+2 x-1) $$

Short Answer

Expert verified
The simplified expression is \(-30x^2 - 12x + 6\).

Step by step solution

01

Apply the Distributive Property

The problem asks to multiply \(-6(5x^2 + 2x - 1)\). The distributive property tells us to multiply \(-6\) by each term inside the parentheses. The expression then becomes:\[-6 \times 5x^2 + (-6) \times 2x + (-6) \times (-1)\].
02

Multiply -6 by Each Term

Now let's multiply \(-6\) by each term:- The first term: \(-6 \times 5x^2 = -30x^2\).- The second term: \(-6 \times 2x = -12x\).- The third term: \(-6 \times (-1) = 6\).
03

Combine All Results

Put together all the terms we obtained:\[ -30x^2 - 12x + 6 \].

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.

Polynomial Multiplication
Polynomial multiplication involves distributing each term in one polynomial to every term in another polynomial.
This method extends the distributive property, which tells us how to multiply a single term across multiple terms inside a parenthesis.
  • In the given expression \(-6(5x^2 + 2x - 1)\), the \(-6\) will multiply each term within the parenthesis.
  • Thus, each term in the polynomial is multiplied individually by \(-6\).
  • The first term becomes \(-6 \times 5x^2 = -30x^2\).
  • The second term becomes \(-6 \times 2x = -12x\).
  • The third term becomes \(-6 \times (-1) = 6\).
This step-by-step application of the distributive property ensures that no term is left out.
When you've multiplied the terms, combine them into one expression.
This final collection of terms is often simplified to give the final result.
Negative Numbers
Negative numbers are essential when dealing with expressions that involve subtraction or multiplication by negative values.
  • Multiplying a negative number by a positive number results in a negative product. For example, \(-6 \times 5 = -30\).
  • When multiplying two negative numbers, the result is positive. For instance, \(-6 \times -1 = 6\).
  • Remembering these rules can help you avoid common mistakes like getting the wrong sign in your results.
The example highlights how each term changes.
By consistently applying these rules, you'll be able to correctly solve any similar problems involving negative multipliers.
Basic Algebra
Basic algebra involves understanding variables, constants, and the rules that govern their interactions.
This foundational concept aids in simplifying expressions, solving equations, and manipulating terms.
  • In the expression \(-6(5x^2 + 2x - 1)\), \(x\) is the variable, while \(-6, 5, 2,\) and \(-1\) are constants.
  • Variables represent unknown quantities and are often paired with coefficients, like in \(5x^2\) where \(5\) is the coefficient.
  • Basic algebra teaches us how to handle expressions by following rules such as the distributive property.
When combining terms, ensure they are like terms. This means they should have the same variable raised to the same power, like \(-30x^2\) and \(-12x\) which cannot be directly combined due to differing powers.
Getting comfortable with these elemental aspects of algebra will help in tackling more complex equations and 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

Solve and graph the solution set. In addition, present the solution set in interval notation. $$ 2 x-1<5 \text { and } 3 x-1<10 $$

The sum of three consecutive odd integers is \(45 .\) Find the integers.

Set up a compound inequality for the following and then solve. If two times an angle is between 180 degrees and 270 degrees, then what are the bounds of the original angle?

The sum of \(4 x\) and 3 is equal to the difference of \(7 x\) and 8 .

Set up a compound inequality for the following and then solve. The perimeter of a square must be between 40 feet and 200 feet. Find the length of all possible sides that satisfy this condition.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

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.