/*! 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 49 Find each product. $$\left(x^{... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 49

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

Short Answer

Expert verified
The product \( (x^{2}+y^{2})^{2} \) is equal to \(x^{4} + 2x^{2}y^{2} + y^{4}\).

Step by step solution

01

Write the Expression as the Product of Two Binomials

Rewrite \( (x^{2}+y^{2})^{2} \) as \( (x^{2} + y^{2}) \cdot (x^{2} + y^{2}) \).
02

Use the Distributive Property

Expand the product using the distributive property, i.e., first multiply each term in the first binomial by each term in the second binomial. This results in \( (x^{2} \cdot x^{2}) + (x^{2} \cdot y^{2}) + (y^{2} \cdot x^{2}) + (y^{2} \cdot y^{2}) \).
03

Simplify the Terms

Simplify each term to obtain \( x^{4} + x^{2}y^{2} + x^{2}y^{2} + y^{4} \) .
04

Combine Like Terms

Now observe that \( x^{2}y^{2} \) is repeated twice. Therefore, combine these two terms to obtain the final solution: \( x^{4} + 2x^{2}y^{2} + y^{4} \).

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

Find each of the products in parts (a)-(c). a. \((x-1)(x+1)\) b. \((x-1)\left(x^{2}+x+1\right)\) c. \((x-1)\left(x^{3}+x^{2}+x+1\right)\) d. Using the pattern found in parts (a)-(c), find $(x-1)\left(x^{4}+x^{3}+x^{2}+x+1\right) without actually multiplying.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. It is not possible to write a binomial with degree \(0 .\)

In Exercises \(85-86,\) the variable \(n\) in each exponent represents a natural Number. Divide the polynomial by the monomial. Then use polynomial multiplication to check the quotient. $$\frac{12 x^{15 n}-24 x^{12 n}+8 x^{3 n}}{4 x^{3 n}}$$

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

In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{8 x^{6} y^{3}-12 x^{8} y^{2}-4 x^{14} y^{6}}{-4 x^{6} y^{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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.