/*! 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 87 Perform the indicated operation ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 87

Perform the indicated operation or operations. $$(2 x+5)(2 x-5)\left(4 x^{2}+25\right)$$

Short Answer

Expert verified
The solution is: \(16x^4 - 625\).

Step by step solution

01

Distribute the First Two Terms

Distribute the first two terms, \(2x+5\) and \(2x-5\), using the distributive property (also known as the FOIL method for two binomials). FOIL stands for First, Outer, Inner, Last. Let's multiply:\n \[(2 x+5)(2 x-5)= 4x^2 - 25\]
02

Distribute the Result with the Third Term

Now, distribute \(4x^2 - 25\) with the third term \(4x^2 + 25\). This multiplication will be simpler if treated as the multiplication of two binomials where the only difference is the sign.\n \[(4x^2 -25)(4x^2 + 25)=16x^4 - 625\]
03

Conclusion

The multiplication of all three terms \((2 x+5)(2 x-5)(4 x^{2}+25)\) yields the solution \(16x^4 - 625\).

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

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\left\\{-9,-\frac{4}{5}, 0,0.25, \sqrt{3}, 9.2, \sqrt{100}\right\\}$$

$$\text { Factor completely.}$$ $$10 x^{2}(x+1)-7 x(x+1)-6(x+1)$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-4(x-y), \text { for } x=8 \text { and } y=3$$

Find the intersection of the sets. $$\\{0,1,3,5\\} \cap\\{-5,-3,-1\\}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Decision 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.