Multiplying power point ms.johnson
•Download as PPT, PDF•
0 likes•154 views
This document provides steps for multiplying a binomial and a trinomial. It instructs the reader to first draw a grid and label it with the terms of each factor. Then it shows filling in the grid by multiplying corresponding terms and collecting like terms. The final step is writing the completely multiplied expression.
Report
Share
Report
Share
Recommended
Power point
This document provides steps for multiplying a binomial and a trinomial. It instructs the user to first label a grid with the terms of each expression. Then, it says to add the side numbers with the top numbers, finding matching variables and adding them up. Finally, the multiplied expression is written as the sum of terms with matching variables that have been added together.
Powerpoint2
To multiply a binomial and a trinomial, put each term of the expressions in their own box in a multiplication table. Then multiply corresponding terms together and combine like terms from smallest to largest exponent order. For example, (2d^2 +8d+5)(6d+7) is multiplied out to get 12d^3 +23d^2 +86d+35 by placing each term in a box and multiplying across.
1.3 Solving Linear Equations
1) The document provides examples of solving linear equations involving fractions.
2) Several multi-step linear equations are solved through addition, subtraction, multiplication and division.
3) The solutions are provided after showing the step-by-step work.
Review Sheet B Substitution And Solving Inequalities
The document contains a review sheet on substitution and solving inequalities with 10 problems. It begins with 4 problems simplifying expressions using substitution when given a value for the variable. It then has 2 problems solving one-step inequalities and 2 problems solving two-step inequalities. It concludes with a problem to graph an inequality.
Oct.25
The document provides instructions and examples for solving equations for variables. It begins with warm-up exercises solving equations for m and a. For the equation 3m - n = k, the steps are shown to isolate m as m = 2k + n/3. For the equation 6 - ay = 4(a - b), the steps factorize the right side and isolate a as a = (6 + 4b)/(4 + y). The document concludes with an announcement of a final exam review.
Arithmetic
This document provides an overview of arithmetic operators and operations in C++. It discusses the different arithmetic operators, order of operations, integer and decimal division, data types and order, and type casting. It explains that integer division drops the decimal, while operations involving doubles will result in decimal numbers. It also outlines that the order of operations is parentheses first, then multiplication/division/modulus, followed by addition/subtraction. Type casting can be used to change the resulting data type of an operation.
Maths: Order of Operations
This document provides a series of math problems involving operations like multiplication, division, addition, subtraction, exponents, and order of operations. It begins with warmup problems calculating square numbers and expressions using the order of operations from BIMDAS. Subsequent sections include evaluating expressions, determining if equations are true or false, filling in missing numbers, and creating an original equation with given numbers and an answer of 2. The final section provides a link to an external math test.
Answers
The document contains examples of numerical patterns with rules for continuing the pattern. Each section provides a starting pattern, the rule for continuing it, and asks the reader to determine the next two numbers in the pattern and identify the rule. Patterns include adding a constant like 2 or 3 to the previous number, or adding a constant like 4 or 2 to a running total to determine the perimeter of a shape.
Recommended
Power point
This document provides steps for multiplying a binomial and a trinomial. It instructs the user to first label a grid with the terms of each expression. Then, it says to add the side numbers with the top numbers, finding matching variables and adding them up. Finally, the multiplied expression is written as the sum of terms with matching variables that have been added together.
Powerpoint2
To multiply a binomial and a trinomial, put each term of the expressions in their own box in a multiplication table. Then multiply corresponding terms together and combine like terms from smallest to largest exponent order. For example, (2d^2 +8d+5)(6d+7) is multiplied out to get 12d^3 +23d^2 +86d+35 by placing each term in a box and multiplying across.
1.3 Solving Linear Equations
1) The document provides examples of solving linear equations involving fractions.
2) Several multi-step linear equations are solved through addition, subtraction, multiplication and division.
3) The solutions are provided after showing the step-by-step work.
Review Sheet B Substitution And Solving Inequalities
The document contains a review sheet on substitution and solving inequalities with 10 problems. It begins with 4 problems simplifying expressions using substitution when given a value for the variable. It then has 2 problems solving one-step inequalities and 2 problems solving two-step inequalities. It concludes with a problem to graph an inequality.
Oct.25
The document provides instructions and examples for solving equations for variables. It begins with warm-up exercises solving equations for m and a. For the equation 3m - n = k, the steps are shown to isolate m as m = 2k + n/3. For the equation 6 - ay = 4(a - b), the steps factorize the right side and isolate a as a = (6 + 4b)/(4 + y). The document concludes with an announcement of a final exam review.
Arithmetic
This document provides an overview of arithmetic operators and operations in C++. It discusses the different arithmetic operators, order of operations, integer and decimal division, data types and order, and type casting. It explains that integer division drops the decimal, while operations involving doubles will result in decimal numbers. It also outlines that the order of operations is parentheses first, then multiplication/division/modulus, followed by addition/subtraction. Type casting can be used to change the resulting data type of an operation.
Maths: Order of Operations
This document provides a series of math problems involving operations like multiplication, division, addition, subtraction, exponents, and order of operations. It begins with warmup problems calculating square numbers and expressions using the order of operations from BIMDAS. Subsequent sections include evaluating expressions, determining if equations are true or false, filling in missing numbers, and creating an original equation with given numbers and an answer of 2. The final section provides a link to an external math test.
Answers
The document contains examples of numerical patterns with rules for continuing the pattern. Each section provides a starting pattern, the rule for continuing it, and asks the reader to determine the next two numbers in the pattern and identify the rule. Patterns include adding a constant like 2 or 3 to the previous number, or adding a constant like 4 or 2 to a running total to determine the perimeter of a shape.
Three step problem
The document provides a 3-step process for multiplying a binomial and a trinomial. Step 1 involves multiplying out each term of the binomial and trinomial. Step 2 combines the results into a single expression. Step 3 collects like terms by adding coefficients with the same exponent. The example provided shows multiplying (17d10 + 12d2 + 9) and (31d9 + 21), resulting in an expression with 6 terms that are not combined further.
Guide to multiplying a binomial and a trinomial powerpoint
To multiply a binomial and a trinomial, order the terms by descending exponent, multiply the coefficients and add the exponents of like terms, then combine the terms in descending exponent order. Specifically, (5x^6 + 9x^3 + 3x)(8x^5 + 3x^4) = 40x^11 + 15x^10 + 72x^8 + 27x^7 + 24x^6 + 9x^5.
4th chapter test for grade v
This document appears to be a summative test for a 1st grade class. It contains 20 multiple choice questions testing math concepts like fractions, multiplication, division, and word problems. It also contains 15 math problems involving fractions, products, and quotients that students are asked to solve on the back of the paper.
Subtracting Numbers with Regrouping
Subtraction with regrouping is done when the ones digit of the minuend is less than the ones digit in the subtrahend.
Regrouping is done by renaming the minuend with more than 10 ones.
Trial terengganu 2014 spm add math k2 skema
The document contains the marking scheme for a mathematics exam paper with multiple questions. Some key details:
- Question 1 involves solving a pair of simultaneous equations to find values of x and y.
- Question 2 relates to graphing quadratic functions and finding maximum points.
- Question 3 covers topics like summation, mean, and solving linear equations.
- Later questions involve additional topics like calculus, trigonometry, and probability.
- The last question requires integrating an expression to find displacement over time for a moving object.
physics
The document provides steps to solve physics problems involving calculating velocity (V) given an initial velocity (332 m/s), a temperature change (20 °C), and a coefficient (0.6 m/s/°C) for increasing velocity with increasing temperature. It then works through using the formula V=332 + (0.6*20) = 344 m/s to calculate velocity for a 20°C increase. It also works through using the formula V=d/t, where d is distance and t is time, to calculate distance given velocity (332 m/s) and time (12.3s) as 4083.6 m.
JUEC 初中 (2014 Past Year)
The document provides information about sets A, B, and C with various element counts and intersections. It states that nA = 28, nB = 25, nC = 20, nA ∩ B = 12, nB ∩ C = 8, nC ∩ A = 9, and nA ∪ B ∪ C = 46. It then asks to find the value of nA ∩ B ∩ C.
Order of Operations
The document discusses the proper order of operations when evaluating mathematical expressions. It states that you should first solve any expressions within parentheses, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right. It then works through examples step-by-step to demonstrate this order of operations.
Operaciones combinadas- Potencias y raices
This document provides instructions for solving multi-step math problems in Spanish:
1. Separate the terms
2. Solve expressions within parentheses
3. Perform exponents and roots
4. Solve multiplication and division
5. Perform addition and subtraction
It then works through several example multi-step math problems step-by-step in Spanish.
Multiplying Trinomials and Binomials
To multiply a binomial and a trinomial, follow these steps:
1) Make a 3x2 table with the monomials along the outside and multiply across and down to fill in the boxes.
2) Write the equation using the numbers from the table.
3) Combine like terms to get the final equation.
F 1-mathematics-paper-form-1-mid-term-2-exam-2017
This document contains instructions for a mathematics exam for Form One students. It has two sections, with Section I containing 16 compulsory short-answer questions and Section II containing 5 questions out of which students must answer any 5. The instructions specify how to show working, which calculators and tables can be used, and other exam guidelines. It provides spaces below each question for students to write their answers and working.
Teoria de exponentes
This document contains a list of group members and examples of exponent exercises. It introduces concepts of exponents and provides step-by-step workings for solving equations involving exponents. Sample exercises include simplifying expressions like 2^x(8+16), solving equations such as x^x/x^3=25, and determining exponent values that satisfy equations such as 2^x=8.
How to factor
This document provides steps for factoring a quadratic equation of the form ax^2 + bx + c. It uses the example equation 2x^2 + 15x + 18. The steps are: 1) Identify the coefficients a, b, c. 2) Multiply a and c and add to b to find the first two terms' common factor. 3) Group the terms and factorize the equation into the form (ax + b)(cx + d). The example is factorized as (1x+6)(2x+3).
q1
This document contains 20 multiple choice questions testing concepts in complex numbers and operations. The questions cover topics such as simplifying complex expressions, adding, subtracting and multiplying complex numbers, evaluating complex functions, finding conjugates and inverses, graphing complex numbers on an Argand diagram, and properties of complex exponents.
transformadores
The document summarizes the analysis of two electrical circuits represented by meshes 1 and 2. It shows the steps taken to solve for the voltage (V1, V2) and current (I1, I2) in each mesh. The analysis involves setting up equations for each mesh based on Kirchhoff's laws, then solving the equations simultaneously to find the voltage and current values. The calculated values for V1, V2, I1, and I2 are reported.
Process permissions
Process permissions allow users to view case objects like dynaforms and documents without modifying cases. Permissions are defined for a user or group and include settings like the case status, target task, accessible objects, and permission type (view or block). Examples demonstrate assigning permissions for specific users to view objects from certain tasks when the case is completed. The document provides details on viewing accessible objects and how permissions control access.
October Can\'t Wait
OCW is a call to action; a movement to bring continual awareness to breast cancer throughout the year. Through our partnerships with various organizations, companies and individuals, Karen Y Buster aims to utilize her artwork to change the way women relate to breast cancer and increase the number of women who are proactively dealing with the disease.
More Related Content
What's hot
Three step problem
The document provides a 3-step process for multiplying a binomial and a trinomial. Step 1 involves multiplying out each term of the binomial and trinomial. Step 2 combines the results into a single expression. Step 3 collects like terms by adding coefficients with the same exponent. The example provided shows multiplying (17d10 + 12d2 + 9) and (31d9 + 21), resulting in an expression with 6 terms that are not combined further.
Guide to multiplying a binomial and a trinomial powerpoint
To multiply a binomial and a trinomial, order the terms by descending exponent, multiply the coefficients and add the exponents of like terms, then combine the terms in descending exponent order. Specifically, (5x^6 + 9x^3 + 3x)(8x^5 + 3x^4) = 40x^11 + 15x^10 + 72x^8 + 27x^7 + 24x^6 + 9x^5.
4th chapter test for grade v
This document appears to be a summative test for a 1st grade class. It contains 20 multiple choice questions testing math concepts like fractions, multiplication, division, and word problems. It also contains 15 math problems involving fractions, products, and quotients that students are asked to solve on the back of the paper.
Subtracting Numbers with Regrouping
Subtraction with regrouping is done when the ones digit of the minuend is less than the ones digit in the subtrahend.
Regrouping is done by renaming the minuend with more than 10 ones.
Trial terengganu 2014 spm add math k2 skema
The document contains the marking scheme for a mathematics exam paper with multiple questions. Some key details:
- Question 1 involves solving a pair of simultaneous equations to find values of x and y.
- Question 2 relates to graphing quadratic functions and finding maximum points.
- Question 3 covers topics like summation, mean, and solving linear equations.
- Later questions involve additional topics like calculus, trigonometry, and probability.
- The last question requires integrating an expression to find displacement over time for a moving object.
physics
The document provides steps to solve physics problems involving calculating velocity (V) given an initial velocity (332 m/s), a temperature change (20 °C), and a coefficient (0.6 m/s/°C) for increasing velocity with increasing temperature. It then works through using the formula V=332 + (0.6*20) = 344 m/s to calculate velocity for a 20°C increase. It also works through using the formula V=d/t, where d is distance and t is time, to calculate distance given velocity (332 m/s) and time (12.3s) as 4083.6 m.
JUEC 初中 (2014 Past Year)
The document provides information about sets A, B, and C with various element counts and intersections. It states that nA = 28, nB = 25, nC = 20, nA ∩ B = 12, nB ∩ C = 8, nC ∩ A = 9, and nA ∪ B ∪ C = 46. It then asks to find the value of nA ∩ B ∩ C.
Order of Operations
The document discusses the proper order of operations when evaluating mathematical expressions. It states that you should first solve any expressions within parentheses, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right. It then works through examples step-by-step to demonstrate this order of operations.
Operaciones combinadas- Potencias y raices
This document provides instructions for solving multi-step math problems in Spanish:
1. Separate the terms
2. Solve expressions within parentheses
3. Perform exponents and roots
4. Solve multiplication and division
5. Perform addition and subtraction
It then works through several example multi-step math problems step-by-step in Spanish.
Multiplying Trinomials and Binomials
To multiply a binomial and a trinomial, follow these steps:
1) Make a 3x2 table with the monomials along the outside and multiply across and down to fill in the boxes.
2) Write the equation using the numbers from the table.
3) Combine like terms to get the final equation.
F 1-mathematics-paper-form-1-mid-term-2-exam-2017
This document contains instructions for a mathematics exam for Form One students. It has two sections, with Section I containing 16 compulsory short-answer questions and Section II containing 5 questions out of which students must answer any 5. The instructions specify how to show working, which calculators and tables can be used, and other exam guidelines. It provides spaces below each question for students to write their answers and working.
Teoria de exponentes
This document contains a list of group members and examples of exponent exercises. It introduces concepts of exponents and provides step-by-step workings for solving equations involving exponents. Sample exercises include simplifying expressions like 2^x(8+16), solving equations such as x^x/x^3=25, and determining exponent values that satisfy equations such as 2^x=8.
How to factor
This document provides steps for factoring a quadratic equation of the form ax^2 + bx + c. It uses the example equation 2x^2 + 15x + 18. The steps are: 1) Identify the coefficients a, b, c. 2) Multiply a and c and add to b to find the first two terms' common factor. 3) Group the terms and factorize the equation into the form (ax + b)(cx + d). The example is factorized as (1x+6)(2x+3).
q1
This document contains 20 multiple choice questions testing concepts in complex numbers and operations. The questions cover topics such as simplifying complex expressions, adding, subtracting and multiplying complex numbers, evaluating complex functions, finding conjugates and inverses, graphing complex numbers on an Argand diagram, and properties of complex exponents.
transformadores
The document summarizes the analysis of two electrical circuits represented by meshes 1 and 2. It shows the steps taken to solve for the voltage (V1, V2) and current (I1, I2) in each mesh. The analysis involves setting up equations for each mesh based on Kirchhoff's laws, then solving the equations simultaneously to find the voltage and current values. The calculated values for V1, V2, I1, and I2 are reported.
What's hot (15)
Guide to multiplying a binomial and a trinomial powerpoint
Guide to multiplying a binomial and a trinomial powerpoint
Viewers also liked
Process permissions
Process permissions allow users to view case objects like dynaforms and documents without modifying cases. Permissions are defined for a user or group and include settings like the case status, target task, accessible objects, and permission type (view or block). Examples demonstrate assigning permissions for specific users to view objects from certain tasks when the case is completed. The document provides details on viewing accessible objects and how permissions control access.
October Can\'t Wait
OCW is a call to action; a movement to bring continual awareness to breast cancer throughout the year. Through our partnerships with various organizations, companies and individuals, Karen Y Buster aims to utilize her artwork to change the way women relate to breast cancer and increase the number of women who are proactively dealing with the disease.
Direct Hit Power Point Presentation
DirectHit is a diagnostic test panel developed by CCC Diagnostics to predict patient response to breast cancer treatments. It analyzes multiple biomarkers from tissue samples using quantitative immunofluorescence to determine effectiveness of hormonal therapies, targeted drugs like Trastuzumab, and chemotherapy drugs. DirectHit aims to personalize treatment selection by identifying ineffective treatments upfront, improving outcomes and reducing costs compared to standard testing methods. CCC Diagnostics is currently expanding DirectHit to additional cancers and chemotherapy drugs based on promising early results.
How to win Second Place in the District Evaluation Contest
This document provides tips for winning second place in an evaluation contest by summarizing advice given by TM Ohmi. Some key points include:
- Evaluators must summarize their comments in the judging criteria, so evaluations should be shorter than usual. Improvement points are especially important to focus on.
- Competitors should observe many contests to understand what types of evaluations tend to win and what test speeches are like. They should also practice evaluating one speech per day.
- Effective evaluations include 2 good points and 1 improvement point, follow a flow from introducing confusion to convincing conclusions, and maximize the density of strong language within strict time limits.
- Competitors should prepare for any type of test speech, including
Judge training
The document outlines the training for contest judges. It covers fundamentals of judging including being fair, accurate listeners. It discusses barriers to objectivity and requirements for disqualifications. The judging criteria is explained covering speech, language, content and delivery. Guidelines for originality protests are provided. A demonstration speech contest is held where trainees judge 3 speakers. Finally, there is discussion around the results and consistency of judging.
論評のエッセンス
This document discusses effective evaluation techniques for speeches given at Toastmasters meetings. It recommends that evaluations be specific by focusing on 2-3 things the speaker did well and 1-2 areas for improvement. Evaluations should also be constructive and reference the speaker's goals to help them continue improving their skills. The ideal evaluation is delivered within 3 minutes using the TimeToaster online timer tool to help ensure conciseness.
Social Realism
Social Realism is an artistic movement, expressed in the visual and other realist arts, which depicts social and racial injustice, economic hardship, through unvarnished pictures of life's struggles.
Viewers also liked (18)
How to win Second Place in the District Evaluation Contest
How to win Second Place in the District Evaluation Contest
Recently uploaded
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
CACJapan - GROUP Presentation 1- Wk 4.pdf
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Assessment and Planning in Educational technology.pptx
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.
Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcThe Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Types of Herbal Cosmetics its standardization.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
A Strategic Approach: GenAI in Education
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaA Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Recently uploaded (20)
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
Assessment and Planning in Educational technology.pptx
Assessment and Planning in Educational technology.pptx
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptx
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Multiplying power point ms.johnson
- 1. Guide to Multiplying a Binomial and a Trinomial (9d^2+6d^7+3)(6d-3)
- 2. Step 1: First you draw your grid
- 3. Step 2: Next you label your grid 9d^7 36d^3 +3 6d -3 54d^8 36d^3 18d -27d^7 -18d^2 -9