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    COURSE INTRODUCTION
    Course Syllabus
    Unit 1: Number Properties
    Unit 1 Learning Outcomes
    1.1: Variables, Constants, and Coefficients
    Identifying Variable Parts and Coefficients of Terms
    1.2: Replacing Variables with Their Values
    How to Write Multiplication in Algebra
    Practice Evaluating Expressions in One Variable
    Practice Evaluating Expressions in Two Variables
    1.3: Order of Operations Review
    Order of Operations
    Practice Using PEMDAS
    1.4: Commutative Property of Addition and Multiplication
    Commutative Law of Addition
    Commutative Law of Multiplication
    1.5: Associative Property of Addition and Multiplication
    Associative Law of Addition
    Associative Property of Multiplication
    1.6: Distributive Property of Multiplication over Addition/Subtraction
    Distributive Property of Multiplication over Addition
    1.7: Definition and Examples of Like Terms
    Like Terms
    1.8: Simplifying Expressions by Combining Like Terms
    Combining Like Terms
    Combining Like Terms Practice
    Practice Combining Like Terms with Negative Coefficients
    Practice Combining Like Terms with Negative Coefficients and Distribution
    Unit 2: Linear Equations
    Unit 2 Learning Outcomes
    2.1: Definition of an Equation and a Solution of an Equation
    Language of Equations
    Testing Solutions to Equations
    Let's Practice Solutions to Equations
    2.2: Addition/Subtraction Property of Equations
    The Subtraction and Addition Properties of Equality
    One-Step Addition and Subtraction Equations
    2.3: Multiplication/Division Property of Equations
    The Division and Multiplication Properties of Equality
    2.4: Equations of the Form ax + b = c
    Solving More Complicated Equations
    Two-Step Equations with Fractions
    Practice Solving Two-Step Equations
    2.5: Equations with Variables on Both Sides
    Equations with Variables on Both Sides
    Practice Solving Equations with Variables on Both Sides
    2.6: Equations with Parentheses
    Solving Equations with the Distributive Property
    Practice Solving Multistep Equations with Distribution
    Number of Solutions
    2.7: Solving Literal Equation for One of the Variables
    Solving Linear Equations with One Variable
    Solving for One Variable
    Practice Solving Literal Equations
    Unit 3: Word Problems
    Unit 3 Learning Outcomes
    3.1: Mathematical Symbols and Expressions for Common Words and Phrases
    Translating Words into Mathematical Symbols
    3.2: Translating Verbal Expression into Mathematical Equations
    Writing Algebraic Expressions
    3.3: Consecutive Integer Problems
    Solving Algebraic Expressions and Equations
    Two-Step Word Problems
    Garden Word Problem
    Business Word Problem
    Two-Step Equations Word Problems Practice
    3.4: Number Problems
    Adding Consecutive and Odd Integers
    Practice Solving Consecutive Integer Problems
    3.5: General Statement Problems
    Solving Linear Word Problems with Substitution
    Simple Word Problems Resulting in Linear Equations
    3.6: Applying the Uniform Motion Equation
    Using the Distance Formula to Solve Word Problems
    3.7: Value Mixture Problems
    Mixture Problems
    Solving Mixture Word Problems
    Practice Solving Mixture Word Problems
    Solving Percent Word Problems
    Practice Solving Percent Word Problems
    Unit 4: Inequalities
    Unit 4 Learning Outcomes
    4.1: Definition and Notation of an Inequality
    Using the Language of Algebra
    4.2: Graphing Inequalities on a Number Line
    Plotting Inequalities on a Number Line
    Introduction to Linear Inequalities
    4.3: Solving One-Step Inequalities
    One-Step Inequalities
    One-Step Inequalities Word Problems
    Practice Solving One-Step Inequalities
    4.4: Solving Multi-Step Inequalities
    Multi-Step Inequalities with Variables on Both Sides
    Inequalities with Variables on Both Sides
    Multi-Step Inequalities
    Practice Solving Multi-Step Inequalities
    Using Inequalities to Solve Word Problems
    Practice Solving Inequality Word Problems
    Unit 5: Graphs of Linear Equations and Inequalities
    Unit 5 Learning Outcomes
    5.1: Graphing Points in the Rectangular Coordinate Plane
    Points in the Coordinate Plane
    Linear Equations Introduction
    5.2: Ordered Pairs as Solutions of an Equation in Two Variables
    Ordered Pair Solutions to Equations
    Graphing Ordered Pair Solutions to Equations
    Practice Ordered Pair Solutions to Linear Equations
    5.3: Graphing Equations in Two Variables of the Form ax + by = c
    Graphing Linear Equations with Two Variables
    5.4: Intercepts of a Line
    Graphs with Intercepts
    5.5: Definition of Slope and Slope Formula
    Understanding the Slope of a Line
    Slopes That Intercept
    Practice with the Slope of a Line
    5.6: Slopes of Parallel and Perpendicular Lines
    Parallel and Perpendicular Lines
    Parallel and Perpendicular Lines from Graph
    Practice with Parallel and Perpendicular Lines
    5.7: Graphing Equations in Two Variables of the Form y = mx + b
    Using the Slope-Intercept Form of an Equation of a Line
    5.8: Point-Slope Form
    Linear Equations in Point-Slope Form
    5.9: Graphing Linear Inequality of Two Variables on the Coordinate Plane
    Graphs of Linear Inequalities
    Represent Relationships between Two Variables with Inequalities to Solve Problems
    Practice Graphing Linear Inequalities
    Unit 6: Systems of Linear Equations and Inequalities
    Unit 6 Learning Outcomes
    6.1: Solution of a System of Linear Equations
    Checking Solutions for Systems of Linear Equations
    6.2: Solving Systems of Linear Equations by Graphing
    Using Graphs to Solve Linear Equations
    6.3: Solving Systems of Linear Equations Using the Substitution Method
    Using the Substitution Method
    Practice Using the Substitution Method
    6.4: Solving Systems of Linear Equations Using the Elimination Method
    The Elimination Method
    Practice Solving Linear Equations with Elimination
    6.5: Strategy for Solving Systems of Linear Equations: Choosing a Method
    Comparing Methods for Solving Linear Systems
    6.6: Solving Word Problems by Using Systems of Equations
    Coin and Mixture Problems
    Solving Word Problems with Linear Systems
    6.7: Graphing Systems of Linear Inequalities
    Graphing Systems of Linear Inequalities
    6.8: Applications of Systems of Linear Inequalities
    Linear Programming
    Unit 7: Operations with Monomials
    Unit 7 Learning Outcomes
    7.1: Algebraic Exponential Expressions
    Exponential Expressions
    7.2: Quotient of Exponents and Power of a Quotient
    Exponential Properties Involving Quotients
    7.3: Negative Exponents
    Negative Exponent Intuition
    Practicing Exponents
    Practice Solving Problems with Negative Exponents
    7.4: Multiplying Monomials
    Multiplication Properties of Exponents
    7.5: Dividing Monomials
    Dividing Monomials
    Unit 8: Operations with Polynomials
    Unit 8 Learning Outcomes
    8.1: Classifying Polynomials
    Introduction to Polynomials
    8.2: Adding and Subtracting Polynomials
    Adding and Subtracting Polynomials
    Adding Polynomials
    Subtracting Polynomials
    8.3: Multiplying a Polynomial by a Monomial
    Multiplying Monomials by Polynomials
    8.4: Multiplying Binomials (FOIL)
    Using the FOIL Technique to Multiply Binomials
    Multiplying Binomials by a Binomial
    8.5: Complete the Square and Difference of Two Squares
    Finding the Square of a Binomial with One Variable
    Special Products of Polynomials
    8.6: Multiplying Polynomials with Any Number of Terms
    Multiplying a Polynomial by a Binomial
    Multiplying Polynomials
    8.7: Dividing a Polynomial by a Monomial
    Dividing Polynomials with Monomials with Remainder
    Dividing Polynomials
    8.8: Dividing a Polynomial by a Binomial
    Dividing Polynomials by Binomials
    Unit 9: Factoring Polynomials
    Unit 9 Learning Outcomes
    9.1: Identifying the Greatest Common Factor (GCF) of Two or More Monomials and Other Expressions
    The Language of Factoring
    Using the Greatest Common Factor and Factor by Grouping
    9.2: Factoring Polynomials by Grouping
    Factoring by Grouping
    Practice Factoring Polynomials by Grouping
    9.3: Revisiting FOIL: Working Backwards
    Basic Concepts Involved in Factoring Trinomials
    9.4: Factoring Trinomials of the Form x² + bx + c When c Is Positive
    Factoring Trinomials
    9.5: Factoring Trinomials of the Form x² + bx + c When c Is Negative
    Factoring Trinomials of the Form x² + bx+ c, Where c is Negative
    Practice Factoring Trinomials
    9.6: Factoring Trinomials of the Form x² + bxy + cy² and ax² + bxy + cy²
    Factoring Trinomials with Two Variables
    Factoring Two-Variable Quadratics
    Practice Factoring Trinomials with Two Variables
    9.7: Identifying and Factoring Complete Square Trinomials
    Factoring Using Perfect Square Trinomials
    Factoring Perfect Square Trinomials
    9.8: Identifying and Factoring Difference of Two Squares
    Factoring Using Difference of Squares
    9.9: Factoring General Polynomials
    Factoring General Polynomials
    More on Factoring General Polynomials
    Practice Factoring General Polynomials
    9.10: Principle of Zero Product and Identifying Solutions
    Using the Principle of Zero Product to Solve Quadratic Equations
    9.11: Using Factoring to Solve Quadratic Equations
    Using Factoring to Solve Quadratic Equations
    More on Using Factoring to Solve Quadratic Equations
    9.12: Solving Application Problems
    Using Factoring to Solve Problems
    Study Guide
    MA007 Study Guide
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    MA007: Certificate Final Exam
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  1. MA007: Algebra
  2. Unit 9: Factoring Polynomials
  3. 9.6: Factoring Trinomials of the Form x² + bxy + cy² and ax² + bxy + cy²
  4. Factoring Two-Variable Quadratics

Factoring Two-Variable Quadratics

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In this example, notice how we can rewrite the problem to make it much easier to work with. Again, this is very similar to factoring in one variable.



Source: Khan Academy, https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-factoring-polynomials-quadratic-forms/v/factoring-quadratics-with-two-variables-example, https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-factoring-polynomials-quadratic-forms/v/factoring-trinomials-by-grouping-1
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.