/*! 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 88 Perform the indicated operation ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 88

Perform the indicated operation or operations. $$(3 x+4)(3 x-4)\left(9 x^{2}+16\right)$$

Short Answer

Expert verified
The solution for the multiplication of expressions \( (3x+4)(3x-4)(9x^{2}+16) \) is \( 81x^{4} - 256 \).

Step by step solution

01

Multiply First Two Binomial Expressions

Start by multiplying the first two binomial expressions. They are in the form of (a+b)(a-b), which is a difference of squares and results in \(a^{2}-b^{2}\). In this case, \(a=3x\) and \(b=4\). So, the result of multiplying them would be \((3x)^{2}-(4)^{2}= 9x^{2} - 16\)
02

Multiply the Result of Step 1 with the Quadratic Expression

Multiply the resulting expression from Step 1, \(9x^{2} - 16\), with the quadratic expression given, \(9x^{2} + 16\). The resulting expression takes the form of \((a+b)(a-b)\) as well, where \(a = 9x^{2}\) and \(b = 16\). Hence, the final product would be \((9x^{2})^{2} - (16)^{2} = 81x^{4} - 256\).
03

Verify Your Answer

To confirm your answer is correct, ensure your final expression matches the form of \(a^{4} - b^{2}\), which represents the difference of two squares. Specifically, the difference of the squares of the squared form in the respective binomials multiplied. In this case, \(a = 9x^{2}\) and \(b = 16\). Therefore, the resulting expression should be \(81x^{4} - 256\).

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 makes sense or does not make sense, and explain your reasoning. The rational expressions $$\frac{7}{14 x} \text { and } \frac{7}{14+x}$$ can both be simplified by dividing each numerator and each denominator by 7

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although I can solve \(3 x+\frac{1}{5}=\frac{1}{4}\) by first subtracting \(\frac{1}{5}\) from both sides, I find it easier to begin by multiplying both sides by \(20,\) the least common denominator.

Perform the indicated operations. Simplify the result, if possible. $$\frac{1}{x^{2}-2 x-8} \div\left(\frac{1}{x-4}-\frac{1}{x+2}\right)$$

When graphing the solutions of an inequality, what does a parenthesis signify? What does a square bracket signify?

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.