/*! 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 97 Factor and simplify each algebra... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 97

Factor and simplify each algebraic expression. $$(x+3)^{\frac{1}{2}}-(x+3)^{\frac{3}{2}}$$

Short Answer

Expert verified
The factored and simplified form of the given algebraic expression is \( (x+3)^{\frac{1}{2}} \left( -x- 2 \right) \)

Step by step solution

01

Identify common base

In the expression, both terms have \( (x+3) \) as the base. So, write down the equation as it is, \((x+3)^{\frac{1}{2}}-(x+3)^{\frac{3}{2}}\)
02

Factor out the common base

Factor out the term with the lowest power, which is \( (x+3)^{\frac{1}{2}} \), from the expression. This results in \( (x+3)^{\frac{1}{2}} \left[ 1- (x+3) \right] \)
03

Simplify the expression

Upon simplifying the terms inside the square brackets, we get \( (x+3)^{\frac{1}{2}} \left[ 1- x- 3 \right] = (x+3)^{\frac{1}{2}} \left[ -x- 2 \right] \)

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{2 x-1}{x-7}+\frac{3 x-1}{x-7}-\frac{5 x-2}{x-7}=0$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \((2 x-3)^{2}=25\) is equivalent to \(2 x-3=5\).

Place the correct symbol, \(>\) or \(<\), in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. \(a, 3^{\frac{1}{2}}\square 3^{1}\) b. \(\sqrt{7}+\sqrt{18} \square \sqrt{7+18}\)

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$ 2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right) $$

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.