/*! 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 61 Find each product. $$\left(3 x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 61

Find each product. $$\left(3 x y^{2}-4 y\right)\left(3 x y^{2}+4 y\right)$$

Short Answer

Expert verified
The product of the given expression is \(9x^2y^4 - 16y^2\)

Step by step solution

01

Multiply The First Terms

The first terms are \(3 xy^2 \) in each binomial. So, we multiply them to get \( (3xy^2) * (3xy^2) = 9x^2y^4 \)
02

Multiply The Outside Terms

The outside terms are \(3xy^2\) from the first binomial and \(4y\) from the second. We multiply them to get \( (3xy^2) * 4y = 12x y^3 \)
03

Multiply The Inside Terms

The inside terms are \(-4y\) from the first binomial and \(3xy^2\) from the second. We multiply them to get \( -4y*3xy^2 = -12x y^3 \)
04

Multiply The Last Terms

\(-4y\) in the first binomial and \(4y\) in the second are the last terms, we multiply them to get \( -4y*4y = -16y^2 \)
05

Add all obtained results

After multiplication, we add all the obtained results. This cancels out the middle terms as one is positive and the other is negative leading to: \(9x^2y^4 + 12xy^3 - 12xy^3 -16y^2 = 9x^2y^4 - 16y^2\)

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

How do you know if an exponential expression is simplified?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I wrote a number where there is no advantage to using scientific notation instead of decimal notation.

What polynomial, when divided by \(3 x^{2}\), yields the trinomial \(6 x^{6}-9 x^{4}+12 x^{2}\) as a quotient?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(y-1)\left(y^{2}+y+1\right)=y^{3}-1$$

In Exercises \(79-82,\) simplify each expression. $$\frac{2 x^{3}(4 x+2)-3 x^{2}(2 x-4)}{2 x^{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.