/*! 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 110 Factor completely. $$x^{4}-10 ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 110

Factor completely. $$x^{4}-10 x^{2} y^{2}+9 y^{4}$$

Short Answer

Expert verified
\((x^{2} - 3y^{2})^{2}\)

Step by step solution

01

Identify the squares

Each term in the equation \(x^{4}-10 x^{2} y^{2}+9 y^{4}\) is a square. The first term \(x^{4}\) is \((x^{2})^{2}\), the last term \(9 y^{4}\) is \((3y^{2})^{2}\) and the middle term \(10 x^{2} y^{2}\) is \(2*(x^{2})*(3y^{2})\). This confirms that the equation can be written in the form of a perfect square trinomial \(a^{2} - 2ab + b^{2}\).
02

Write equation as a perfect square trinomial

From Step 1, we have \(a = x^{2}\) and \(b = 3y^{2}\). Substituting these into the formula of the perfect square trinomial, we get: \((x^{2})^{2} - 2*x^{2}*3y^{2} + (3y^{2})^{2}\)
03

Factor the perfect square trinomial

The equation, being already identified as a perfect square trinomial, can be factored into \((a - b)^{2}\), which turns out to be \((x^{2} - 3y^{2})^{2}\)
04

Factor further (if possible)

The expression \((x^{2} - 3y^{2})^{2}\) itself cannot be factored further using integers because it is a difference of squares where the square root of one of the squares is not an integer.

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

In more U.S. marriages, spouses have different faiths. The bar graph shows the percentage of households with an interfaith marriage in 1988 and \(2012 .\) Also shown is the percentage of households in which a person of faith is married to someone with no religion. The formula $$ I=\frac{1}{4} x+26 $$ models the percentage of U.S. households with an interfaith marriage, \(I, x\) years after \(1988 .\) The formula $$ N=\frac{1}{4} x+6 $$ models the percentage of U.S households in which a person of faith is married to someone with no religion, \(N, x\) years after \(1988 .\) Use these models to solve Exercises \(107-108\). The formula for converting Celsius temperature, \(C,\) to Fahrenheit temperature, \(F\), is $$ F=\frac{9}{5} C+32 $$ If Fahrenheit temperature ranges from \(41^{\circ}\) to \(50^{\circ},\) inclusive, what is the range for Celsius temperature? Use interval notation to express this range.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A local bank charges \(\$ 8\) per month plus 5垄 per check. The credit union charges \(\$ 2\) per month plus 8垄 per check. How many checks should be written each month to make the credit union a better deal?

Explain how to find the least common denominator for denominators of \(x^{2}-100\) and \(x^{2}-20 x+100\).

Describe ways in which solving a linear inequality is different than solving a linear equation.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$\frac{7 x}{x+3}+\frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\).
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Mechanics 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.