/*! 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 28 Factor. $$x^{2}+6 x y+9 y^{2}$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 28

Factor. $$x^{2}+6 x y+9 y^{2}$$

Short Answer

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

Step by step solution

01

Identify the Square Terms

The given expression is a polynomial in the form \(x^{2}+6 x y+9 y^{2}\). The square terms are (\(x^{2}\)) and (\(9y^{2}\)), which can be rewritten as \((x)^{2}+(3y)^{2}\). This indicates that \(a = x\) and \(b = 3y\).
02

Identify the Middle Term

The middle term is (6xy), which can also be written as 2 * a * b, where a is the square root of \(x^{2}\) which is \(x\), and b is the square root of \(9y^{2}\) which is \(3y\). This confirms that the expression is in the format of a perfect square trinomial \(ax^{2} + 2ab + b^{2}\).
03

Apply the Perfect Square Trinomial Factoring Rule

Having identified the values for \(a\) and \(b\), we can apply the perfect square trinomial factoring rule, which results in \((a + b)^{2}\). Substituting \(a = x\) and \(b = 3y\) we get: \((x+3y)^{2}\).

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

For Exercises 78 to \(131,\) factor completely. $$3 a^{2}-24 a b-99 b^{2}$$

For Exercises 140 to \(143,\) find all integers \(k\) such that the trinomial can be factored over the integers. $$y^{2}+4 y+k$$

For Exercises 78 to \(131,\) factor completely. $$5 x^{3}+30 x^{2} y+40 x y^{2}$$

Factor by grouping. $$6 a^{2}+23 a+21$$

Factor by grouping. $$15 a^{4}+26 a^{3}+7 a^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.