/*! 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 98 Factor and simplify each algebra... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 98

Factor and simplify each algebraic expression. $$\left(x^{2}+4\right)^{\frac{3}{2}}+\left(x^{2}+4\right)^{\frac{7}{2}}$$

Short Answer

Expert verified
The simplified form of the given algebraic expression is \(\left(x^{2}+4\right)^{\frac{3}{2}}\left(1+x^{4}+8x^{2}+16\right)\).

Step by step solution

01

Identify Common Terms

Firstly, examine the given expression to identify any common terms between the two parts of the equation. We can see that \(\left(x^{2}+4\right)\) is common in both terms.
02

Factor Out the Shared Base

Once we've identified the common term, which is \(\left(x^{2}+4\right)\), we factor it out. Since the lowest exponent is \(\frac{3}{2}\), that's what we factor out. This gives us \(\left(x^{2}+4\right)^{\frac{3}{2}}\left(1+\left(x^{2}+4\right)^2\right)\).
03

Simplify the Parentheses

Now, simplify the equation in the parentheses. In this case, expanding the binomial \(\left(x^{2}+4\right)^2\) results in \(x^{4}+8x^{2}+16\). This yields our final, simplified expression: \(\left(x^{2}+4\right)^{\frac{3}{2}}\left(1+x^{4}+8x^{2}+16\right)\).

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

Perform the indicated operations. Simplify the result, if possible. $$\frac{a b}{a^{2}+a b+b^{2}}+\left(\frac{a c-a d-b c+b d}{a c-a d+b c-b d} \div \frac{a^{3}-b^{3}}{a^{3}+b^{3}}\right)$$

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

This will help you prepare for the material covered in the next section. Evaluate $$\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}$$ for \(a=2, b=9,\) and \(c=-5\)

What is the discriminant and what information does it provide about a quadratic equation?

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied 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.