/*! 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 64 Simplify each algebraic expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 64

Simplify each algebraic expression. \(14 x^{2}+5-\left[7\left(x^{2}-2\right)+4\right]\)

Short Answer

Expert verified
The simplified form of the given algebraic expression is \(7*x^{2} - 5\)

Step by step solution

01

Distribute the '7' throughout the expression in brackets

In this step, we need to distribute the '7' to both \(x^{2}\) and '-2' in the expression. The distribution rule in algebra states that when you have a multiplier outside a bracket, you can remove the bracket by multiplying each term inside the bracket by the multiplier. So, it becomes \(7*x^{2} - 7*2\), which simplifies to \(7*x^{2} - 14\). This process transforms the expression into: \(14 * x^{2} + 5 - (7 * x^{2} - 14 + 4)\)
02

Combine like terms

The next step is to combine like terms. There are two terms involving \(x^{2}\) in the expression: \(14*x^{2}\) and \(7*x^{2}\). As they are separated by a negative sign we will subtract the terms as follows: \(14*x^{2} - 7*x^{2}\) results in \(7*x^{2}\). Secondly, we will deal with the constants, (5, -14, 4). These are all constants, so we can combine these terms as follows, \(5-14+4\), which equals -5. Now, the expression becomes \(7*x^{2} - 5\)
03

Simplify the expression

Once you have combined like terms, the expression is already in its simplest form: \(7*x^{2} - 5\). In this case, the final term is a constant, so the final stage does not involve any further operations.

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 quadratic equations by factoring. \(2 x^{2}=7 x+4\)

The radicand of the quadratic formula, \(b^{2}-4 a c\), can be used to determine whether \(a x^{2}+b x+c=0\) has solutions that are rational, irrational, or not real numbers. Explain how this works. Is it possible to determine the kinds of answers that one will obtain to a quadratic equation without actually solving the equation? Explain.

Solve the equations using the quadratic formula. \(x^{2}+6 x-10=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-9 x-36\)

Solve the quadratic equations by factoring. \(x^{2}+9 x=-8\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.