practice and homework lesson 6.6 answer key

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Spectrum Math Grade 6 Answer Key Online Pdf | Spectrum Math 6th Grade Answers

Spectrum Math Grade 6 Workbook Answer Key  is available here. So, all the students of grade 6 who are looking for the Spectrum Math 6th Grade Solution Key can get them on this page. Here students and teachers can find the solutions for pretest, posttest, and mid-tests with an explanation. Spectrum Math Answer Key for Grade 6 is a great way of learning essential math skills like-wise word problems, order of operations, and Solving Word Problems.

Spectrum Math 6th Grade Answer Key | Spectrum Math Workbook Grade 6 Answer Key

Support your child’s math educational journey with our Spectrum Math Grade 6 Answer Key . This is the place where your child can learn fundamental math concepts in a fun and simple manner. Each and every question in Spectrum Math Workbook Grade 6 Answer Key is prepared by the math experts. So, we suggest all the 6th graders make use of our Spectrum Math 6th Grade Answers Chapter-wise by clicking on the below attached links.

Spectrum Math Grade 6 Answer Key Online Chapter 1 Understanding the Number System and Operations

• Spectrum Math Grade 6 Chapter 1 Pretest
• Lesson 1.1 Number Properties
• Lesson 1.2 The Distributive Property
• Lesson 1.3 Multi-Digit Multiplication
• Lesson 1.4 Multi-Digit Division
• Lesson 1.5 Reciprocal Operations
• Lesson 1.6 Problem Solving
• Lesson 1.7 Greatest Common Factor
• Lesson 1.8 Least Common Multiple
• Lesson 1.9 Multiplying Decimals
• Lesson 1.10 Dividing by Two Digits
• Lesson 1.11 Problem Solving
• Spectrum Math Grade 6 Chapter 1 Posttest

Spectrum Math Grade 6 Answers Chapter 2 Multiplying and Dividing Fractions

• Spectrum Math Grade 6 Chapter 2 Pretest
• Lesson 2.1 Multiplying Fractions and Mixed Numbers
• Lesson 2.2 Using Visual Models to Divide Fractions
• Lesson 2.3 Dividing Fractions
• Lesson 2.4 Dividing Mixed Numbers
• Lesson 2.5 Problem Solving
• Spectrum Math Grade 6 Chapter 2 Posttest

Spectrum Math 6th Grade Answer Key Chapter 3 Ratios, Rates, and Percents

• Spectrum Math Grade 6 Chapter 3 Pretest
• Lesson 3.1 Understanding Ratios
• Lesson 3.2 Solving Ratios
• Lesson 3.3 Solving Ratio Problems
• Lesson 3.4 Understanding Unit Rates
• Lesson 3.5 Problem Solving
• Lesson 3.6 Understanding Percents
• Lesson 3.7 Finding Percents Using Fractions
• Lesson 3.8 Finding Percents Using Decimals
• Lesson 3.9 Finding Percents
• Lesson 3.10 Problem Solving
• Spectrum Math Grade 6 Chapter 3 Posttest

Spectrum Math 6th Grade Answers Chapter 4 Integer Concepts

• Spectrum Math Grade 6 Chapter 4 Pretest
• Lesson 4.1 Integers as Opposite Numbers
• Lesson 4.2 Integer Values in Real Life
• Lesson 4.3 Absolute Value
• Lesson 4.4 Comparing and Ordering Integers
• Lesson 4.5 Using Integers in the Coordinate Plane
• Lesson 4.6 Problem Solving in the Coordinate Plane
• Spectrum Math Grade 6 Chapter 4 Posttest

Spectrum Math Grade 6 Chapters 1-4 Mid-Test

Spectrum Math Workbook Grade 6 Answer Key Pdf Chapter 5 Expressions and Equations

• Spectrum Math Grade 6 Chapter 5 Pretest
• Lesson 5.1 Using Exponents
• Lesson 5.2 Parts of an Expression
• Lesson 5.3 Writing Expressions
• Lesson 5.4 Equivalent Expressions
• Lesson 5.5 Solving 1-Step Equations: Addition & Subtraction
• Lesson 5.6 Solving 1-Step Equations: Multiplication & Division
• Lesson 5.7 Problem Solving
• Lesson 5.8 Solving Inequalities
• Lesson 5.9 Dependent and Independent Variables
• Spectrum Math Grade 6 Chapter 5 Posttest

Spectrum 6th Grade Math Workbook Chapter 6 Geometry

• Spectrum Math Grade 6 Chapter 6 Pretest
• Lesson 6.1 Calculating Area: Triangles
• Lesson 6.2 Calculating Area: Quadrilaterals
• Lesson 6.3 Calculating Area: Other Polygons
• Lesson 6.4 Volume of Rectangular Solids
• Lesson 6.5 Problem Solving
• Lesson 6.6 Surface Area: Rectangular Solids
• Lesson 6.7 Surface Area: Pyramids
• Lesson 6.8 Graphing Polygons: Rectangles
• Lesson 6.9 Graphing Polygons: Right Triangles
• Spectrum Math Grade 6 Chapter 6 Posttest

Spectrum Math Grade 6 Book Free Download Chapter 7 Probability and Statistics

• Spectrum Math Grade 6 Chapter 7 Pretest
• Lesson 7.1 Asking Statistical Questions
• Lesson 7.2 Describing Data
• Lesson 7.3 Measures of Center: Mean
• Lesson 7.4 Measures of Center: Median
• Lesson 7.5 Measures of Center: Mode
• Lesson 7.6 Finding Measures of Center
• Lesson 7.7 Using Measures of Center
• Lesson 7.8 Measures of Variability: Range
• Lesson 7.9 Measures of Variability: Interquartile Range
• Lesson 7.10 Measures of Variability: Mean Absolute Deviation
• Lesson 7.11 Using Measures of Variability
• Lesson 7.12 Plotting Data: Stem-and-Leaf Plots
• Lesson 7.13 Plotting Data: Box-and-Whisker Plots
• Lesson 7.14 Plotting Data: Line Graphs
• Lesson 7.15 Plotting Data: Histograms
• Lesson 7.16 Summarizing Data Sets
• Spectrum Math Grade 6 Chapter 7 Posttest

Spectrum Math Grade 6 Chapters 1-7 Final Test

FAQs on Spectrum Math Grade 6 Solution Key

1. How to access the Spectrum Math Grade 6 Answer Key pdf?

It is very simple to get access to the pdf formatted Spectrum Math Workbook 6th Grade Solution Key Offline. Just tap the link you like to practice and download the pdf for free.

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3. Is it possible to score high by solving Spectrum Math Grade 6 Answer Key?

Yes, our Spectrum Math 6th Grade Answer Key helps the students to understand the concepts well and enhance their skills which helps the 6th graders to score good marks on the exams.

We believe that the information shown above is beneficial for all the 6th graders. Our aim is to support the students to learn the math concepts in a simple manner and become a pro. We are always ready to clarify your doubts. So feel free to post the comments regarding the questions on Spectrum Math Answer Key for 6th Grade. Stay tuned to our ccssmathanswers.com to get all the updates on Spectrum Math Grade Solutions Chapter-wise.

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Go Math Answer Key for Grade K, 1, 2, 3, 4, 5, 6, 7, and 8

Go Math Answer Key:  HMH Go Math Answer Key for Grade K, 1, 2, 3, 4, 5, 6, 7, and 8 are provided helps students to have learning targets and achieve success at chapter and lesson level and makes learning visible.

Download Go Math Answer Key for Grades K-8 | HMH Go Math Solution Key for Grades Kindergarten, 1, 2, 3, 4, 5, 6, 7, 8

All the Concepts in the CCSS Go Math Answer Key for Grades Kindergarten, 1, 2, 3, 4, 5, 6, 7, 8 are given with straightforward and detailed descriptions.

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Free Download Go Math Answer Key from Kindergarten to 8th Grade

Students can find Go Math Answer Keys right from  Primary School to High School all in one place. You just need to tap on the quick links available in order to access them and learn all the Chapters in each grade. Once you tap on the quick link you will be directed to the respective Grade Solutions Key wherein you can access the complete information. You can find Solutions for all the Go Math Textbook Questions free of cost and we don’t charge any amount.

• Go Math Kindergarten Answer Key

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Go Math Grade K Answer Key

• Chapter 1 Represent, Count, and Write Numbers 0 to 5
• Chapter 2 Compare Numbers to 5
• Chapter 3 Represent, Count, and Write Numbers 6 to 9
• Chapter 4 Represent and Compare Numbers to 10
• Chapter 5 Addition
• Chapter 6 Subtraction
• Chapter 7 Represent, Count, and Write 11 to 19
• Chapter 8 Represent, Count, and Write 20 and Beyond
• Chapter 9 Identify and Describe Two-Dimensional Shapes
• Chapter 10 Identify and Describe Three-Dimensional Shapes
• Chapter 11 Measurement
• Chapter 12 Classify and Sort Data
• Chapter 1 Addition Concepts
• Chapter 2 Subtraction Concepts
• Chapter 3 Addition Strategies
• Chapter 4 Subtraction Strategies
• Chapter 5 Addition and Subtraction Relationships
• Chapter 6 Count and Model Numbers
• Chapter 7 Compare Numbers
• Chapter 8 Two-Digit Addition and Subtraction
• Chapter 9 Measurement
• Chapter 10 Represent Data
• Chapter 11 Three-Dimensional Geometry
• Chapter 12 Two-Dimensional Geometry
• Chapter 1 Number Concepts
• Chapter 2 Numbers to 1,000
• Chapter 3 Basic Facts and Relationships
• Chapter 4 2-Digit Addition
• Chapter 5 2-Digit Subtraction
• Chapter 6 3-Digit Addition and Subtraction
• Chapter 7 Money and Time
• Chapter 8 Length in Customary Units
• Chapter 9 Length in Metric Units
• Chapter 10 Data
• Chapter 11 Geometry and Fraction Concepts

Grade 3 HMH Go Math – Answer Keys

• Chapter 1: Addition and Subtraction within 1,000
• Chapter 2: Represent and Interpret Data
• Chapter 3: Understand Multiplication
• Chapter 4: Multiplication Facts and Strategies
• Chapter 5: Use Multiplication Facts
• Chapter 6: Understand Division
• Chapter 7: Division Facts and Strategies
• Chapter 8: Understand Fractions
• Chapter 9: Compare Fractions
• Chapter 10: Time, Length, Liquid Volume, and Mass
• Chapter 11: Perimeter and Area
• Chapter 12:Two-Dimensional Shapes

Grade 3 HMH Go Math – Extra Practice Questions and Answers

• Chapter 1: Addition and Subtraction within 1,000 Extra Practice
• Chapter 2: Represent and Interpret Data Extra Practice
• Chapter 3: Understand Multiplication Extra Practice
• Chapter 4: Multiplication Facts and Strategies Extra Practice
• Chapter 5: Use Multiplication Facts Extra Practice
• Chapter 6: Understand Division Extra Practice
• Chapter 7: Division Facts and Strategies Extra Practice
• Chapter 8: Understand Fractions Extra Practice
• Chapter 9: Compare Fractions Extra Practice
• Chapter 10: Time, Length, Liquid Volume, and Mass Extra Practice
• Chapter 11: Perimeter and Area Extra Practice
• Chapter 12: Two-Dimensional Shapes Extra Practice

Common Core Grade 4 HMH Go Math – Answer Keys

• Chapter 1 Place Value, Addition, and Subtraction to One Million
• Chapter 2 Multiply by 1-Digit Numbers
• Chapter 3 Multiply 2-Digit Numbers
• Chapter 4 Divide by 1-Digit Numbers
• Chapter 5 Factors, Multiples, and Patterns
• Chapter 6 Fraction Equivalence and Comparison
• Chapter 7 Add and Subtract Fractions
• Chapter 8 Multiply Fractions by Whole Numbers
• Chapter 9 Relate Fractions and Decimals
• Chapter 10 Two-Dimensional Figures
• Chapter 11 Angles
• Chapter 12Relative Sizes of Measurement Units
• Chapter 13 Algebra: Perimeter and Area

Grade 4 Homework Practice FL.

Common Core – Grade 4 – Practice Book

• Chapter 1 Place Value, Addition, and Subtraction to One Million  (Pages 1- 20)
• Chapter 2 Multiply by 1-Digit Numbers  (Pages 21 – 47)
• Chapter 3 Multiply 2-Digit Numbers  (Pages 49- 65)
• Chapter 4 Divide by 1-Digit Numbers  (Pages 67 – 93)
• Chapter 5 Factors, Multiples, and Patterns  (Pages 95 – 109)
• Chapter 6 Fraction Equivalence and Comparison  (Pages 111 – 129)
• Chapter 7 Add and Subtract Fractions  (Pages 131 – 153)
• Chapter 8 Multiply Fractions by Whole Numbers  (Pages 155- 167)
• Chapter 9 Relate Fractions and Decimals  (Pages 169- 185)
• Chapter 10 Two-Dimensional Figures  (Pages 187- 204)
• Chapter 11 Angles  (Pages 205- 217)
• Chapter 12 Relative Sizes of Measurement Units  (Pages 219- 244)
• Chapter 13 Algebra: Perimeter and Area  (Pages 245- 258)

Grade 4 Homework FL. – Answer Keys

• Chapter 2 Multiply by 1-Digit Numbers Review/Test
• Chapter 3 Multiply 2-Digit Numbers Review/Test
• Chapter 4 Divide by 1-Digit Numbers Review/Test
• Chapter 5 Factors, Multiples, and Patterns Review/Test
• Chapter 6 Fraction Equivalence and Comparison Review/Test
• Chapter 7 Add and Subtract Fractions Review/Test
• Chapter 8 Multiply Fractions by Whole Numbers Review/Test
• Chapter 9 Relate Fractions and Decimals Review/Test
• Chapter 10 Two-Dimensional Figures Review/Test
• Chapter 11 Angles Review/Test
• Chapter 12 Relative Sizes of Measurement Units Review/Test
• Chapter 13 Algebra: Perimeter and Area Review/Test
• Chapter 1: Place Value, Multiplication, and Expressions
• Chapter 2: Divide Whole Numbers
• Chapter 3: Add and Subtract Decimals
• Chapter 4: Multiply Decimals
• Chapter 5: Divide Decimals
• Chapter 6: Add and Subtract Fractions with Unlike Denominators
• Chapter 7: Multiply Fractions
• Chapter 8: Divide Fractions
• Chapter 9: Algebra: Patterns and Graphing
• Chapter 10: Convert Units of Measure
• Chapter 11: Geometry and Volume
• Chapter 1: Divide Multi-Digit Numbers
• Chapter 2: Fractions and Decimals
• Chapter 3: Understand Positive and Negative Numbers
• Chapter 4: Model Ratios
• Chapter 5: Model Percents
• Chapter 6: Convert Units of Length
• Chapter 7: Exponents
• Chapter 8: Solutions of Equations
• Chapter 9: Independent and Dependent Variables
• Chapter 10: Area of Parallelograms
• Chapter 11: Surface Area and Volume
• Chapter 12: Data Displays and Measures of Center
• Chapter 13: Variability and Data Distributions

Go Math Answer Key for Grade 7

• Chapter 1: Adding and Subtracting Integers
• Chapter 2: Multiplying and Dividing Integers
• Chapter 3: Rational Numbers
• Chapter 4: Rates and Proportionality
• Chapter 5: Percent Increase and Decrease
• Chapter 6: Algebraic Expressions
• Chapter 7: Writing and Solving One-Step Inequalities
• Chapter 8: Modeling Geometric Figures
• Chapter 9: Circumference, Area, and Volume
• Chapter 10: Random Samples and Populations
• Chapter 11: Analyzing and Comparing Data
• Chapter 12: Experimental Probability
• Chapter 13: Theoretical Probability and Simulations
• Chapter 1 Real Numbers
• Chapter 2 Exponents and Scientific Notation
• Chapter 3 Proportional Relationships
• Chapter 4 Nonproportional Relationships
• Chapter 5 Writing Linear Equations
• Chapter 6 Functions
• Chapter 7 Solving Linear Equations
• Chapter 8 Solving Systems of Linear Equations
• Chapter 9 Transformations and Congruence
• Chapter 10 Transformations and Similarity
• Chapter 11 Angle Relationships in Parallel Lines and Triangles
• Chapter 12 The Pythagorean Theorem
• Chapter 13 Volume
• Chapter 14 Scatter Plots
• Chapter 15 Two-Way Tables

Give your kid the right amount of knowledge he needs as a part of your preparation by taking the help of our HMH Go Math Answer Key for Grades K-8. Resolve all your queries and assess your preparation standard using the Common Core Go Math Solution Key.

Practicing from the Go Math Answer Key for Grades K to 8 will provide a grade by grade roadmap and prepares students for College Readiness. Gradewise HMH Go Math Answer Key provided will develop problem-solving skills among students thereby helping them to Think, Explore and Grow. The Diverse Opportunities provided helps Kids to master the content with engaging activities.

Characteristics of Go Math Answer Key for Grades K to 8

Go through the below-listed features of referring to the HMH Go Math Anwer Key for Grades K to 8. They are outlined as follows

• All the Go Math Answer Key for Grades K to 8 are easy to download and we don’t charge any penny from you.
• Step by Step Solutions provided in the HMH Go Math Practice Key is aligned as per the College and Career Expectations.
• Solving from the Math 101 Practice Key helps you inculcate Higher Order Thinking Skills and you can answer any Question from your Homework, Assessment, or Review Test.
• More Rigorous Content made available meets the Common Core State Standards Initiative.
• You can gain a deeper knowledge of mathematical concepts and find solutions to all the Questions from Go Math Textbooks for Grades K, 1, 2, 3, 4, 5, 6, 7, 8

FAQs on Common Core HMH Go Math Answer Key

1. When Can I use the Go Math Answer Key for Grades K-8?

You can use the HMH Go Math Answer Key for Grades K to 8 while practicing the Go Math Textbook Questions as a part of your Homework or Assessment and make the most out of them.

2. Is there any site that provides the Common Core Go Math Solutions Key for Grades K, 1, 2, 3, 4, 5, 6, 7, 8?

Yes, you can find Go Math Answer Key for Grades K, 1, 2, 3, 4, 5, 6, 7, 8 all in one place i.e. ccssmathanswers.com a trusted and reliable portal.

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Yes, you can download the HMH Math 101 Practice Key for free on our page via quick links available and we don’t charge any amount for it.

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Go Math! 6 Common Core Edition, Grade: 6 Publisher: Houghton Mifflin Harcourt

Go math 6 common core edition, title : go math 6 common core edition, publisher : houghton mifflin harcourt, isbn : 547587783, isbn-13 : 9780547587783, use the table below to find videos, mobile apps, worksheets and lessons that supplement go math 6 common core edition..

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5 m 2 5 m 2

3 y 2 ( 3 x + 2 x 2 + 7 y ) 3 y 2 ( 3 x + 2 x 2 + 7 y )

3 p ( p 2 − 2 p q + 3 q 2 ) 3 p ( p 2 − 2 p q + 3 q 2 )

2 x 2 ( x + 6 ) 2 x 2 ( x + 6 )

3 y 2 ( 2 y − 5 ) 3 y 2 ( 2 y − 5 )

3 x y ( 5 x 2 − x y + 2 y 2 ) 3 x y ( 5 x 2 − x y + 2 y 2 )

2 a b ( 4 a 2 + a b − 3 b 2 ) 2 a b ( 4 a 2 + a b − 3 b 2 )

−4 b ( b 2 − 4 b + 2 ) −4 b ( b 2 − 4 b + 2 )

−7 a ( a 2 − 3 a + 2 ) −7 a ( a 2 − 3 a + 2 )

( m + 3 ) ( 4 m − 7 ) ( m + 3 ) ( 4 m − 7 )

( n − 4 ) ( 8 n + 5 ) ( n − 4 ) ( 8 n + 5 )

( x + 8 ) ( y + 3 ) ( x + 8 ) ( y + 3 )

( a + 7 ) ( b + 8 ) ( a + 7 ) ( b + 8 )

ⓐ ( x − 5 ) ( x + 2 ) ( x − 5 ) ( x + 2 ) ⓑ ( 5 x − 4 ) ( 4 x − 3 ) ( 5 x − 4 ) ( 4 x − 3 )

ⓐ ( y + 4 ) ( y − 7 ) ( y + 4 ) ( y − 7 ) ⓑ ( 7 m − 3 ) ( 6 m − 5 ) ( 7 m − 3 ) ( 6 m − 5 )

( q + 4 ) ( q + 6 ) ( q + 4 ) ( q + 6 )

( t + 2 ) ( t + 12 ) ( t + 2 ) ( t + 12 )

( u − 3 ) ( u − 6 ) ( u − 3 ) ( u − 6 )

( y − 7 ) ( y − 9 ) ( y − 7 ) ( y − 9 )

( m + 3 ) ( m + 6 ) ( m + 3 ) ( m + 6 )

( n − 3 ) ( n − 4 ) ( n − 3 ) ( n − 4 )

( a − b ) ( a − 10 b ) ( a − b ) ( a − 10 b )

( m − n ) ( m − 12 n ) ( m − n ) ( m − 12 n )

5 x ( x − 1 ) ( x + 4 ) 5 x ( x − 1 ) ( x + 4 )

6 y ( y − 2 ) ( y + 5 ) 6 y ( y − 2 ) ( y + 5 )

( a + 1 ) ( 2 a + 3 ) ( a + 1 ) ( 2 a + 3 )

( b + 1 ) ( 4 b + 1 ) ( b + 1 ) ( 4 b + 1 )

( 2 x − 3 ) ( 4 x − 1 ) ( 2 x − 3 ) ( 4 x − 1 )

( 2 y − 7 ) ( 5 y − 1 ) ( 2 y − 7 ) ( 5 y − 1 )

( 3 x + 2 y ) ( 6 x − 5 y ) ( 3 x + 2 y ) ( 6 x − 5 y )

( 3 x + y ) ( 10 x − 21 y ) ( 3 x + y ) ( 10 x − 21 y )

5 n ( n − 4 ) ( 3 n − 5 ) 5 n ( n − 4 ) ( 3 n − 5 )

8 q ( q + 6 ) ( 7 q − 2 ) 8 q ( q + 6 ) ( 7 q − 2 )

( x + 2 ) ( 6 x + 1 ) ( x + 2 ) ( 6 x + 1 )

( 2 y + 1 ) ( 2 y + 3 ) ( 2 y + 1 ) ( 2 y + 3 )

4 ( 2 x − 3 ) ( 2 x − 1 ) 4 ( 2 x − 3 ) ( 2 x − 1 )

3 ( 3 w − 2 ) ( 2 w − 3 ) 3 ( 3 w − 2 ) ( 2 w − 3 )

( h 2 − 2 ) ( h 2 + 6 ) ( h 2 − 2 ) ( h 2 + 6 )

( y 2 + 4 ) ( y 2 − 5 ) ( y 2 + 4 ) ( y 2 − 5 )

( x − 3 ) ( x − 1 ) ( x − 3 ) ( x − 1 )

( y − 1 ) ( y + 1 ) ( y − 1 ) ( y + 1 )

( 2 x + 3 ) 2 ( 2 x + 3 ) 2

( 3 y + 4 ) 2 ( 3 y + 4 ) 2

( 8 y − 5 ) 2 ( 8 y − 5 ) 2

( 4 z − 9 ) 2 ( 4 z − 9 ) 2

( 7 x + 6 y ) 2 ( 7 x + 6 y ) 2

( 8 m + 7 n ) 2 ( 8 m + 7 n ) 2

2 y ( 2 x − 3 ) 2 2 y ( 2 x − 3 ) 2

3 q ( 3 p + 5 ) 2 3 q ( 3 p + 5 ) 2

( 11 m − 1 ) ( 11 m + 1 ) ( 11 m − 1 ) ( 11 m + 1 )

( 9 y − 1 ) ( 9 y + 1 ) ( 9 y − 1 ) ( 9 y + 1 )

( 16 m − 5 n ) ( 16 m + 5 n ) ( 16 m − 5 n ) ( 16 m + 5 n )

( 11 p − 3 q ) ( 11 p + 3 q ) ( 11 p − 3 q ) ( 11 p + 3 q )

2 y 2 ( x − 2 ) ( x + 2 ) ( x 2 + 4 ) 2 y 2 ( x − 2 ) ( x + 2 ) ( x 2 + 4 )

7 c 2 ( a − b ) ( a + b ) ( a 2 + b 2 ) 7 c 2 ( a − b ) ( a + b ) ( a 2 + b 2 )

( x − 5 − y ) ( x − 5 + y ) ( x − 5 − y ) ( x − 5 + y )

( x + 3 − 2 y ) ( x + 3 + 2 y ) ( x + 3 − 2 y ) ( x + 3 + 2 y )

( x + 3 ) ( x 2 − 3 x + 9 ) ( x + 3 ) ( x 2 − 3 x + 9 )

( y + 2 ) ( y 2 − 2 y + 4 ) ( y + 2 ) ( y 2 − 2 y + 4 )

( 2 x − 3 y ) ( 4 x 2 + 6 x y + 9 y 2 ) ( 2 x − 3 y ) ( 4 x 2 + 6 x y + 9 y 2 )

( 10 m − 5 n ) ( 100 m 2 + 50 m n + 25 n 2 ) ( 10 m − 5 n ) ( 100 m 2 + 50 m n + 25 n 2 )

4 ( 5 p + q ) ( 25 p 2 − 5 p q + q 2 ) 4 ( 5 p + q ) ( 25 p 2 − 5 p q + q 2 )

2 ( 6 c + 7 d ) ( 36 c 2 − 42 c d + 49 d 2 ) 2 ( 6 c + 7 d ) ( 36 c 2 − 42 c d + 49 d 2 )

( −2 y + 1 ) ( 13 y 2 + 5 y + 1 ) ( −2 y + 1 ) ( 13 y 2 + 5 y + 1 )

( −4 n + 3 ) ( 31 n 2 + 21 n + 9 ) ( −4 n + 3 ) ( 31 n 2 + 21 n + 9 )

8 y ( y − 1 ) ( y + 3 ) 8 y ( y − 1 ) ( y + 3 )

5 y ( y − 9 ) ( y + 6 ) 5 y ( y − 9 ) ( y + 6 )

4 x ( 2 x − 3 ) ( 2 x + 3 ) 4 x ( 2 x − 3 ) ( 2 x + 3 )

3 ( 3 y − 4 ) ( 3 y + 4 ) 3 ( 3 y − 4 ) ( 3 y + 4 )

( 2 x + 5 y ) 2 ( 2 x + 5 y ) 2

( 3 x − 4 y ) 2 ( 3 x − 4 y ) 2

2 x y ( 25 x 2 + 36 ) 2 x y ( 25 x 2 + 36 )

3 x y ( 9 y 2 + 16 ) 3 x y ( 9 y 2 + 16 )

2 ( 5 m + 6 n ) ( 25 m 2 − 30 m n + 36 n 2 ) 2 ( 5 m + 6 n ) ( 25 m 2 − 30 m n + 36 n 2 )

2 ( p + 3 q ) ( p 2 − 3 p q + 9 q 2 ) 2 ( p + 3 q ) ( p 2 − 3 p q + 9 q 2 )

4 a b ( a 2 + 4 ) ( a − 2 ) ( a + 2 ) 4 a b ( a 2 + 4 ) ( a − 2 ) ( a + 2 )

7 x y ( y 2 + 1 ) ( y − 1 ) ( y + 1 ) 7 x y ( y 2 + 1 ) ( y − 1 ) ( y + 1 )

6 ( x + b ) ( x − 2 c ) 6 ( x + b ) ( x − 2 c )

2 ( 4 x − 1 ) ( 2 x + 3 y ) 2 ( 4 x − 1 ) ( 2 x + 3 y )

4 q ( p − 3 ) ( p − 1 ) 4 q ( p − 3 ) ( p − 1 )

3 p ( 2 q + 1 ) ( q − 2 ) 3 p ( 2 q + 1 ) ( q − 2 )

( 2 x − 3 y − 5 ) ( 2 x − 3 y + 5 ) ( 2 x − 3 y − 5 ) ( 2 x − 3 y + 5 )

( 4 x − 3 y − 8 ) ( 4 x − 3 y + 8 ) ( 4 x − 3 y − 8 ) ( 4 x − 3 y + 8 )

m = 2 3 , m = − 1 2 m = 2 3 , m = − 1 2

p = − 3 4 , p = 3 4 p = − 3 4 , p = 3 4

c = 2 , c = 4 3 c = 2 , c = 4 3

d = 3 , d = − 1 2 d = 3 , d = − 1 2

p = 7 5 , p = − 7 5 p = 7 5 , p = − 7 5

x = 11 6 , x = − 11 6 x = 11 6 , x = − 11 6

m = 1 , m = 3 2 m = 1 , m = 3 2

k = 3 , k = −3 k = 3 , k = −3

a = − 5 2 , a = 2 3 a = − 5 2 , a = 2 3

b = −2 , b = − 1 20 b = −2 , b = − 1 20

x = 0 , x = 3 2 x = 0 , x = 3 2

y = 0 , y = 1 4 y = 0 , y = 1 4

ⓐ x = −3 x = −3 or x = 5 x = 5 ⓑ ( −3 , 7 ) ( −3 , 7 ) ( 5 , 7 ) ( 5 , 7 )

ⓐ x = 1 x = 1 or x = 7 x = 7 ⓑ ( 1 , −4 ) ( 1 , −4 ) ( 7 , −4 ) ( 7 , −4 )

ⓐ x = 1 x = 1 or x = 5 2 x = 5 2 ⓑ ( 1 , 0 ) , ( 1 , 0 ) , ( 5 2 , 0 ) ( 5 2 , 0 ) ⓒ ( 0 , 5 ) ( 0 , 5 )

ⓐ x = −3 x = −3 or x = 5 6 x = 5 6 ⓑ ( −3 , 0 ) , ( −3 , 0 ) , ( 5 6 , 0 ) ( 5 6 , 0 ) ⓒ ( 0 , −15 ) ( 0 , −15 )

−15 , −17 −15 , −17 and 15, 17

−23 , −21 −23 , −21 and 21, 23

The width is 5 feet and length is 6 feet.

The length of the patio is 12 feet and the width 15 feet.

5 feet and 12 feet

24 feet and 25 feet

ⓐ 5 ⓑ 0;3 ⓒ 196

ⓐ 4 ⓑ 0;2 ⓒ 144

Section 6.1 Exercises

2 p q 2 p q

6 m 2 n 3 6 m 2 n 3

5 x 3 y 5 x 3 y

3 ( 2 m + 3 ) 3 ( 2 m + 3 )

9 ( n − 7 ) 9 ( n − 7 )

3 ( x 2 + 2 x − 3 ) 3 ( x 2 + 2 x − 3 )

2 ( 4 p 2 + 2 p + 1 ) 2 ( 4 p 2 + 2 p + 1 )

8 y 2 ( y + 2 ) 8 y 2 ( y + 2 )

5 x ( x 2 − 3 x + 4 ) 5 x ( x 2 − 3 x + 4 )

3 x ( 8 x 2 − 4 x + 5 ) 3 x ( 8 x 2 − 4 x + 5 )

6 y 2 ( 2 x + 3 x 2 − 5 y ) 6 y 2 ( 2 x + 3 x 2 − 5 y )

4 x y ( 5 x 2 − x y + 3 y 2 ) 4 x y ( 5 x 2 − x y + 3 y 2 )

−2 ( x + 2 ) −2 ( x + 2 )

−2 x ( x 2 − 9 x + 4 ) −2 x ( x 2 − 9 x + 4 )

−4 p q ( p 2 + 3 p q − 4 q ) −4 p q ( p 2 + 3 p q − 4 q )

( x + 1 ) ( 5 x + 3 ) ( x + 1 ) ( 5 x + 3 )

( b − 2 ) ( 3 b − 13 ) ( b − 2 ) ( 3 b − 13 )

( b + 5 ) ( a + 3 ) ( b + 5 ) ( a + 3 )

( y + 5 ) ( 8 y + 1 ) ( y + 5 ) ( 8 y + 1 )

( u + 2 ) ( v − 9 ) ( u + 2 ) ( v − 9 )

( u − 1 ) ( u + 6 ) ( u − 1 ) ( u + 6 )

( 3 p − 5 ) ( 3 p + 4 ) ( 3 p − 5 ) ( 3 p + 4 )

( n − 6 ) ( m − 4 ) ( n − 6 ) ( m − 4 )

( x − 7 ) ( 2 x − 5 ) ( x − 7 ) ( 2 x − 5 )

−9 x y ( 3 x + 2 y ) −9 x y ( 3 x + 2 y )

( x 2 + 2 ) ( 3 x − 7 ) ( x 2 + 2 ) ( 3 x − 7 )

( x + y ) ( x + 5 ) ( x + y ) ( x + 5 )

Answers will vary.

Section 6.2 Exercises

( p + 5 ) ( p + 6 ) ( p + 5 ) ( p + 6 )

( n + 3 ) ( n + 16 ) ( n + 3 ) ( n + 16 )

( a + 5 ) ( a + 20 ) ( a + 5 ) ( a + 20 )

( x − 2 ) ( x − 6 ) ( x − 2 ) ( x − 6 )

( y − 3 ) ( y − 15 ) ( y − 3 ) ( y − 15 )

( x − 1 ) ( x − 7 ) ( x − 1 ) ( x − 7 )

( p − 1 ) ( p + 6 ) ( p − 1 ) ( p + 6 )

( x − 4 ) ( x − 2 ) ( x − 4 ) ( x − 2 )

( x − 12 ) ( x + 1 ) ( x − 12 ) ( x + 1 )

( x + 8 y ) ( x − 10 y ) ( x + 8 y ) ( x − 10 y )

( m + n ) ( m − 65 n ) ( m + n ) ( m − 65 n )

( a + 8 b ) ( a − 3 b ) ( a + 8 b ) ( a − 3 b )

p ( p − 10 ) ( p + 2 ) p ( p − 10 ) ( p + 2 )

3 m ( m − 5 ) ( m − 2 ) 3 m ( m − 5 ) ( m − 2 )

5 x 2 ( x − 3 ) ( x + 5 ) 5 x 2 ( x − 3 ) ( x + 5 )

( 2 t + 5 ) ( t + 1 ) ( 2 t + 5 ) ( t + 1 )

( 11 x + 1 ) ( x + 3 ) ( 11 x + 1 ) ( x + 3 )

( 4 w − 1 ) ( w − 1 ) ( 4 w − 1 ) ( w − 1 )

( 4 q + 1 ) ( q − 2 ) ( 4 q + 1 ) ( q − 2 )

( 2 p − 5 q ) ( 3 p − 2 q ) ( 2 p − 5 q ) ( 3 p − 2 q )

( 4 a − 3 b ) ( a + 5 b ) ( 4 a − 3 b ) ( a + 5 b )

−16 ( x + 1 ) ( x + 1 ) −16 ( x + 1 ) ( x + 1 )

−10 q ( 3 q + 2 ) ( q + 4 ) −10 q ( 3 q + 2 ) ( q + 4 )

( 5 n + 1 ) ( n + 4 ) ( 5 n + 1 ) ( n + 4 )

( 2 k − 3 ) ( 2 k − 5 ) ( 2 k − 3 ) ( 2 k − 5 )

( 3 y + 5 ) ( 2 y − 3 ) ( 3 y + 5 ) ( 2 y − 3 )

( 2 n + 3 ) ( n − 15 ) ( 2 n + 3 ) ( n − 15 )

10 ( 6 y − 1 ) ( y + 5 ) 10 ( 6 y − 1 ) ( y + 5 )

3 z ( 8 z + 3 ) ( 2 z − 5 ) 3 z ( 8 z + 3 ) ( 2 z − 5 )

8 ( 2 s + 3 ) ( s + 1 ) 8 ( 2 s + 3 ) ( s + 1 )

12 ( 4 y − 3 ) ( y + 1 ) 12 ( 4 y − 3 ) ( y + 1 )

( x 2 + 3 ) ( x 2 − 4 ) ( x 2 + 3 ) ( x 2 − 4 )

( x 2 − 7 ) ( x 2 + 4 ) ( x 2 − 7 ) ( x 2 + 4 )

( 3 y − 4 ) ( 3 y − 1 ) ( 3 y − 4 ) ( 3 y − 1 )

( u − 6 ) ( u − 6 ) ( u − 6 ) ( u − 6 )

( r − 4 s ) ( r − 16 s ) ( r − 4 s ) ( r − 16 s )

( 4 y − 7 ) ( 3 y − 2 ) ( 4 y − 7 ) ( 3 y − 2 )

( 2 n − 1 ) ( 3 n + 4 ) ( 2 n − 1 ) ( 3 n + 4 )

13 ( z 2 + 3 z − 2 ) 13 ( z 2 + 3 z − 2 )

3 p ( p + 7 ) 3 p ( p + 7 )

6 ( r + 2 ) ( r + 3 ) 6 ( r + 2 ) ( r + 3 )

4 ( 2 n + 1 ) ( 3 n + 1 ) 4 ( 2 n + 1 ) ( 3 n + 1 )

( x 2 + 2 ) ( x 2 − 6 ) ( x 2 + 2 ) ( x 2 − 6 )

( x − 9 ) ( x + 6 ) ( x − 9 ) ( x + 6 )

Section 6.3 Exercises

( 4 y + 3 ) 2 ( 4 y + 3 ) 2

( 6 s + 7 ) 2 ( 6 s + 7 ) 2

( 10 x − 1 ) 2 ( 10 x − 1 ) 2

( 5 n − 12 ) 2 ( 5 n − 12 ) 2

( 7 x + 2 y ) 2 ( 7 x + 2 y ) 2

( 10 y − 1 ) 2 ( 10 y − 1 ) 2

10 j ( k + 4 ) 2 10 j ( k + 4 ) 2

3 u 2 ( 5 u − v ) 2 3 u 2 ( 5 u − v ) 2

( 5 v − 1 ) ( 5 v + 1 ) ( 5 v − 1 ) ( 5 v + 1 )

( 2 − 7 x ) ( 2 + 7 x ) ( 2 − 7 x ) ( 2 + 7 x )

6 p 2 ( q − 3 ) ( q + 3 ) 6 p 2 ( q − 3 ) ( q + 3 )

6 ( 4 p 2 + 9 ) 6 ( 4 p 2 + 9 )

( 11 x − 12 y ) ( 11 x + 12 y ) ( 11 x − 12 y ) ( 11 x + 12 y )

( 13 c − 6 d ) ( 13 c + 6 d ) ( 13 c − 6 d ) ( 13 c + 6 d )

( 2 z − 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 ) ( 2 z − 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 )

2 b 2 ( 3 a − 2 ) ( 3 a + 2 ) ( 9 a 2 + 4 ) 2 b 2 ( 3 a − 2 ) ( 3 a + 2 ) ( 9 a 2 + 4 )

( x − 8 − y ) ( x − 8 + y ) ( x − 8 − y ) ( x − 8 + y )

( a + 3 − 3 b ) ( a + 3 + 3 b ) ( a + 3 − 3 b ) ( a + 3 + 3 b )

( x + 5 ) ( x 2 − 5 x + 25 ) ( x + 5 ) ( x 2 − 5 x + 25 )

( z 2 − 3 ) ( z 4 + 3 z 2 + 9 ) ( z 2 − 3 ) ( z 4 + 3 z 2 + 9 )

( 2 − 7 t ) ( 4 + 14 t + 49 t 2 ) ( 2 − 7 t ) ( 4 + 14 t + 49 t 2 )

( 2 y − 5 z ) ( 4 y 2 + 10 y z + 25 z 2 ) ( 2 y − 5 z ) ( 4 y 2 + 10 y z + 25 z 2 )

( 6 a + 5 b ) ( 36 a 2 − 30 a b + 25 b 2 ) ( 6 a + 5 b ) ( 36 a 2 − 30 a b + 25 b 2 )

7 ( k + 2 ) ( k 2 − 2 k + 4 ) 7 ( k + 2 ) ( k 2 − 2 k + 4 )

2 x 2 ( 1 − 2 y ) ( 1 + 2 y + 4 y 2 ) 2 x 2 ( 1 − 2 y ) ( 1 + 2 y + 4 y 2 )

9 ( x + 1 ) ( x 2 + 3 ) 9 ( x + 1 ) ( x 2 + 3 )

− ( 3 y + 5 ) ( 21 y 2 − 30 y + 25 ) − ( 3 y + 5 ) ( 21 y 2 − 30 y + 25 )

( 8 a − 5 ) ( 8 a + 5 ) ( 8 a − 5 ) ( 8 a + 5 )

3 ( 3 q − 1 ) ( 3 q + 1 ) 3 ( 3 q − 1 ) ( 3 q + 1 )

( 4 x − 9 ) 2 ( 4 x − 9 ) 2

2 ( 4 p 2 + 1 ) 2 ( 4 p 2 + 1 )

( 5 − 2 y ) ( 25 + 10 y + 4 y 2 ) ( 5 − 2 y ) ( 25 + 10 y + 4 y 2 )

5 ( 3 n + 2 ) 2 5 ( 3 n + 2 ) 2

( x + y − 5 ) ( x − y − 5 ) ( x + y − 5 ) ( x − y − 5 )

( 3 x + 1 ) ( 3 x 2 + 1 ) ( 3 x + 1 ) ( 3 x 2 + 1 )

Section 6.4 Exercises

( 2 n − 1 ) ( n + 7 ) ( 2 n − 1 ) ( n + 7 )

a 3 ( a 2 + 9 ) a 3 ( a 2 + 9 )

( 11 r − s ) ( 11 r + s ) ( 11 r − s ) ( 11 r + s )

8 ( m − 2 ) ( m + 2 ) 8 ( m − 2 ) ( m + 2 )

( 5 w − 6 ) 2 ( 5 w − 6 ) 2

( m + 7 n ) 2 ( m + 7 n ) 2

7 ( b + 3 ) ( b - 2 ) 7 ( b + 3 ) ( b - 2 )

3 x y ( x − 3 ) ( x 2 + 3 x + 9 ) 3 x y ( x − 3 ) ( x 2 + 3 x + 9 )

( k − 2 ) ( k + 2 ) ( k 2 + 4 ) ( k − 2 ) ( k + 2 ) ( k 2 + 4 )

5 x y 2 ( x 2 + 4 ) ( x + 2 ) ( x − 2 ) 5 x y 2 ( x 2 + 4 ) ( x + 2 ) ( x − 2 )

3 ( 5 p + 4 ) ( q − 1 ) 3 ( 5 p + 4 ) ( q − 1 )

4 ( x + 3 ) ( x + 7 ) 4 ( x + 3 ) ( x + 7 )

4 u 2 ( u + 1 ) ( u 2 − u + 1 ) 4 u 2 ( u + 1 ) ( u 2 − u + 1 )

10 ( m − 5 ) ( m + 5 ) ( m 2 + 25 ) 10 ( m − 5 ) ( m + 5 ) ( m 2 + 25 )

3 y ( 3 x + 2 ) ( 4 x − 1 ) 3 y ( 3 x + 2 ) ( 4 x − 1 )

( y + 1 ) ( y − 1 ) ( y 2 − y + 1 ) ( y 2 + y + 1 ) ( y + 1 ) ( y − 1 ) ( y 2 − y + 1 ) ( y 2 + y + 1 )

( 3 x − y + 7 ) ( 3 x − y − 7 ) ( 3 x − y + 7 ) ( 3 x − y − 7 )

( 3 x - 2 ) 2 ( 3 x - 2 ) 2

Section 6.5 Exercises

a = 10 / 3 , a = 7 / 2 a = 10 / 3 , a = 7 / 2

m = 0 , m = 5 / 12 m = 0 , m = 5 / 12

x = 1 / 2 x = 1 / 2

a = −4 5 , a = 6 a = −4 5 , a = 6

m = 5 / 4 , m = 3 m = 5 / 4 , m = 3

a = −1 , a = 0 a = −1 , a = 0

m = 12 / 7 , m = −12 / 7 m = 12 / 7 , m = −12 / 7

y = −9 / 4 , y = 9 / 4 y = −9 / 4 , y = 9 / 4

n = −6 / 11 , n = 6 / 11 n = −6 / 11 , n = 6 / 11

x = 2 , x = −5 x = 2 , x = −5

x = 3 / 2 , x = −1 x = 3 / 2 , x = −1

x = 2 , x = −4 / 3 x = 2 , x = −4 / 3

x = 3 / 2 x = 3 / 2

x = −3 / 2 , x = 1 / 3 x = −3 / 2 , x = 1 / 3

p = 0 , p = ¾ p = 0 , p = ¾

x = 0 , x = 6 x = 0 , x = 6

x = 0 , x = –1 / 3 x = 0 , x = –1 / 3

ⓐ x = 2 x = 2 or x = 6 x = 6 ⓑ ( 2 , −4 ) ( 2 , −4 ) ( 6 , −4 ) ( 6 , −4 )

ⓐ x = 3 2 x = 3 2 or x = 3 4 x = 3 4 ⓑ ( 3 2 , −4 ) ( 3 2 , −4 ) ( 3 4 , −4 ) ( 3 4 , −4 )

ⓐ x = 2 3 x = 2 3 or x = − 2 3 x = − 2 3 ⓑ ( 2 3 , 0 ) ( 2 3 , 0 ) , ( − 2 3 , 0 ) ( − 2 3 , 0 ) ⓒ ( 0 , −4 ) ( 0 , −4 )

ⓐ x = 5 3 x = 5 3 or x = − 1 2 x = − 1 2 ⓑ ( 5 3 , 0 ) ( 5 3 , 0 ) , ( − 1 2 , 0 ) ( − 1 2 , 0 ) ⓒ ( 0 , −5 ) ( 0 , −5 )

−13 , −11 −13 , −11 and 11, 13

−14 , −12 −14 , −12 and 12, 14

Review Exercises

3 a b 2 3 a b 2

7 ( 5 y + 12 ) 7 ( 5 y + 12 )

3 x ( 6 x 2 − 5 ) 3 x ( 6 x 2 − 5 )

4 x ( x 2 − 3 x + 4 ) 4 x ( x 2 − 3 x + 4 )

−3 x ( x 2 − 9 x + 4 ) −3 x ( x 2 − 9 x + 4 )

( a + b ) ( x − y ) ( a + b ) ( x − y )

( x − 3 ) ( x + 7 ) ( x − 3 ) ( x + 7 )

( m 2 + 1 ) ( m + 1 ) ( m 2 + 1 ) ( m + 1 )

( a + 3 ) ( a + 11 ) ( a + 3 ) ( a + 11 )

( m + 9 ) ( m − 6 ) ( m + 9 ) ( m − 6 )

( x + 5 y ) ( x + 7 y ) ( x + 5 y ) ( x + 7 y )

( a + 7 b ) ( a − 3 b ) ( a + 7 b ) ( a − 3 b )

3 y ( y − 5 ) ( y − 2 ) 3 y ( y − 5 ) ( y − 2 )

( 5 y + 9 ) ( y + 1 ) ( 5 y + 9 ) ( y + 1 )

( 5 y + 1 ) ( 2 y − 11 ) ( 5 y + 1 ) ( 2 y − 11 )

−9 ( 9 a − 1 ) ( a + 2 ) −9 ( 9 a − 1 ) ( a + 2 )

( 3 a − 1 ) ( 6 a − 1 ) ( 3 a − 1 ) ( 6 a − 1 )

( 3 x − 1 ) ( 5 x + 2 ) ( 3 x − 1 ) ( 5 x + 2 )

3 ( x + 4 ) ( x − 3 ) 3 ( x + 4 ) ( x − 3 )

3 ( 2 a − 7 ) ( 3 a + 1 ) 3 ( 2 a − 7 ) ( 3 a + 1 )

( x 2 − 15 ) ( x 2 + 2 ) ( x 2 − 15 ) ( x 2 + 2 )

( 5 x + 3 ) 2 ( 5 x + 3 ) 2

10 ( 2 x + 9 ) 2 10 ( 2 x + 9 ) 2

( 13 m + n ) ( 13 m − n ) ( 13 m + n ) ( 13 m − n )

( 3 + 11 y ) ( 3 − 11 y ) ( 3 + 11 y ) ( 3 − 11 y )

n ( 13 n + 1 ) ( 13 n − 1 ) n ( 13 n + 1 ) ( 13 n − 1 )

( a − 5 ) ( a 2 + 5 a + 25 ) ( a − 5 ) ( a 2 + 5 a + 25 )

2 ( m + 3 ) ( m 2 − 3 m + 9 ) 2 ( m + 3 ) ( m 2 − 3 m + 9 )

4 x 2 ( 6 x + 11 ) 4 x 2 ( 6 x + 11 )

( 4 n − 7 m ) 2 ( 4 n − 7 m ) 2

5 u 2 ( u + 3 ) ( u − 3 ) 5 u 2 ( u + 3 ) ( u − 3 )

( b − 4 ) ( b 2 + 4 b + 16 ) ( b − 4 ) ( b 2 + 4 b + 16 )

( 2 b + 5 c ) ( b − c ) ( 2 b + 5 c ) ( b − c )

5 ( q + 3 ) ( q − 6 ) 5 ( q + 3 ) ( q − 6 )

( 4 x − 3 y + 8 ) ( 4 x − 3 y − 8 ) ( 4 x − 3 y + 8 ) ( 4 x − 3 y − 8 )

b = −1 / 5 , b = −1 / 6 b = −1 / 5 , b = −1 / 6

x = −4 , x = −5 x = −4 , x = −5

p = − 5 2 , p = 8 p = − 5 2 , p = 8

m = 5 12 , m = − 5 12 m = 5 12 , m = − 5 12

ⓐ x = −7 x = −7 or x = −4 x = −4 ⓑ ( −7 , −8 ) ( −7 , −8 ) ( −4 , −8 ) ( −4 , −8 )

ⓐ x = 7 8 x = 7 8 or x = − 7 8 x = − 7 8 ⓑ ( 7 8 , 0 ) , ( 7 8 , 0 ) , ( − 7 8 , 0 ) ( − 7 8 , 0 ) ⓒ ( 0 , −49 ) ( 0 , −49 )

The numbers are −21 −21 and −19 −19 or 19 and 21.

The lengths are 8, 15, and 17 ft.

Practice Test

40 a 2 ( 2 + 3 a ) 40 a 2 ( 2 + 3 a )

( x + 7 ) ( x + 6 ) ( x + 7 ) ( x + 6 )

( x − 8 ) ( y + 7 ) ( x − 8 ) ( y + 7 )

( 3 s − 2 ) 2 ( 3 s − 2 ) 2

3 ( x + 5 y ) ( x − 5 y ) 3 ( x + 5 y ) ( x − 5 y )

( 3 x 2 − 5 ) ( 2 x 2 − 3 ) ( 3 x 2 − 5 ) ( 2 x 2 − 3 )

a = 4 / 5 , a = −6 a = 4 / 5 , a = −6

The width is 12 inches and the length is 14 inches.

ⓐ x = 3 x = 3 or x = 4 x = 4 ⓑ ( 3 , −7 ) ( 3 , −7 ) ( 4 , −7 ) ( 4 , −7 )

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Access for free at https://openstax.org/books/intermediate-algebra/pages/1-introduction

• Authors: Lynn Marecek
• Publisher/website: OpenStax
• Book title: Intermediate Algebra
• Publication date: Mar 14, 2017
• Location: Houston, Texas
• Book URL: https://openstax.org/books/intermediate-algebra/pages/1-introduction
• Section URL: https://openstax.org/books/intermediate-algebra/pages/chapter-6

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Answer Key 6.6

• [latex]\begin{array}[t]{ccc} (x)^2&-&(8)^2 \\ x^2&-&64 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (a)^2&-&(4)^2 \\ a^2&-&16 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (1)^2&-&(3p)^2 \\ 1&-&9p^2 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (x)^2&-&(3)^2 \\ x^2&-&9 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (1)^2&-&(7n)^2 \\ 1&-&49n^2 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (8m)^2&-&(5)^2 \\ 64m^2&-&25 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (4y)^2&-&(x)^2 \\ 16y^2&-&x^2 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (7a)^2&-&(7b)^2 \\ 49a^2&-&49b^2 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (4m)^2&-&(8n)^2 \\ 16m^2&-&64n^2 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (3y)^2&-&(3x)^2 \\ 9y^2&-&9x^2 \end{array}[/latex]
• [latex]\begin{array}[t]{ccc} (6x)^2&-&(2y)^2 \\ 36x^2&-&4y^2 \end{array}[/latex]
• [latex]\begin{array}[t]{ccccc} (1)^2&+&2(1)(5n)&+&(5n)^2 \\ 1&+&10n&+&25n^2 \end{array}[/latex]
• [latex]a^2+10a+25[/latex]
• [latex]x^2-16x+64[/latex]
• [latex]1-12n+36n^2[/latex]
• [latex]16x^2-40x+25[/latex]
• [latex]25m^2-80m+64[/latex]
• [latex]9a^2+18ab+9b^2[/latex]
• [latex]25x^2+70xy+49y^2[/latex]
• [latex]16m^2-8mn+n^2[/latex]
• [latex]25+20r+4r^2[/latex]
• [latex]m^2-14m+49[/latex]
• [latex]16v^2-49[/latex]
• [latex]b^2-16[/latex]

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