/*! 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 66 Simplify each algebraic expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 66

Simplify each algebraic expression. \(4\left(6 x^{2}-3\right)-\left[2\left(5 x^{2}-1\right)+1\right]\)

Short Answer

Expert verified
The simplified form of the given algebraic expression is \(14x^{2} - 11\).

Step by step solution

01

Distribute Multiplication Over Addition/Subtraction Inside Parentheses

Distribute the 4 into the first parentheses: \(4*6x^{2} - 4*3 = 24x^{2} - 12\). Distribute the 2 into the second parentheses: \(2*5x^{2} - 2*1 = 10x^{2} - 2\). The expression becomes \(24x^{2} - 12 - (10x^{2} - 2 + 1)\).
02

Simplify the Expression Inside the Second Parentheses

Simplify the expression inside the parentheses: \(10x^{2} - 2 + 1 = 10x^{2} -1\). So now, the expression is \(24x^{2} - 12 - (10x^{2} - 1)\).
03

Apply the Distributive Property to Remove the Parentheses

To remove the parentheses, distribute the minus sign, which means changing the sign of each term inside the parentheses: \(-10x^{2} + 1\). So now, the expression is \(24x^{2} - 12 - 10x^{2} + 1\).
04

Combine like terms

Combine terms that have the same variable part: \(24x^{2} - 10x^{2}=14x^{2}\) and \(-12 +1 = -11\). So, the simplified expression is \(14x^{2} - 11\).

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!

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 the equations using the quadratic formula. \(x^{2}+4 x=6\)

Solve the equations using the quadratic formula. \(x^{2}-5 x=10\)

Solve the equations using the quadratic formula. \(x^{2}+4 x+1=0\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I began the solution of \(5-3(x+2)>10 x\) by simplifying the left side, obtaining \(2 x+4>10 x\).

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In an inequality such as \(5 x+4<8 x-5\), I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure 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.