Warm-Up Multiplying Monomials and Binomials ? Lesson Question Lesson Goals Multiply and binomials. Apply the Identify special products of Determine products . property. using models. W 2K Words to Know Fill in this table as you work through the lesson. You may also use the glossary to help you. the result of a multiplication of two or more terms a number that evenly divides into another number; a polynomial that evenly divides into another polynomial an expression involving a sum of powers in one or more variables multiplied by coefficients, where the powers must be whole numbers the property stating that the product of a factor times a given quantity containing a sum or difference is equal to the sum or difference of the products of that factor times each term from within the quantity © Edgenuity, Inc. 1 Warm-Up Multiplying Monomials and Binomials Using the Distributive Property Use the distributive property to find Distributive property: the product. −4 푥 − 5 푎 푏 + 푐 = −4 푥 + −5 푥 + −4 −5 −4푥 + 20 © Edgenuity, Inc. 2 Instruction Multiplying Monomials and Binomials Slide 2 Multiplication Properties of Polynomials The following multiplication properties are true for any polynomials a, b, and c: Closure property The of two polynomials is a polynomial. Commutative property 푎푏 = Associative property (푎푏)푐 = 푎(푏푐) property 푎(푏 + 푐) = 푎푏 + 푎푐 Using the Distributive Property Multiply: 6푦3(−5푦 + 3) • Product of powers rule: 3 3 6푦 −5푦 + (6푦 )(3) 푎푚 ∙ 푎푛 = + 18푦3 4 Multiplying a Monomial by a Binomial Using Algebra Tiles 2푥 푥 − 2 = − © Edgenuity, Inc. 3 Instruction Multiplying Monomials and Binomials Slide 8 Multiplying Two Binomials Using Algebra Tiles Draw the missing algebra tiles to complete the model. 2푥 − 1)(푥 − 4 2푥2 − + 푥 − 3 푥 + 2 − 3푥 + 2푥 − 푥2 − 푥 − 6 © Edgenuity, Inc. 4 Instruction Multiplying Monomials and Binomials Slide 10 How to Multiply a Binomial by a Binomial Using a Model How to multiply polynomials using a model: 1. Write each factor as headers to a row or column. 2. Multiply each entry by and column. 3. Add the terms inside the model, combining when necessary. 4. Write the resulting polynomial in form. Multiplying a Binomial by a Binomial Using a Table 1. Write each factor as headers to a row Multiply: −2푣 + 1)(3푣 − 5 or column. 2. Multiply each entry by row and 3푣 column. 3. Add the terms inside the model, combining like terms when −6푣2 necessary. 4. Write the resulting polynomial in standard form. +1 −5 = −6푣2 + −5 © Edgenuity, Inc. 5 Instruction Multiplying Monomials and Binomials Slide 12 Multiplying a Binomial by a Binomial Use the property to find the product of −7푛 − 4 and 3 + 2푛. −7푛 − 4 3 + 2푛 −7푛 + −7푛 + −4 + −4 2푛 −21푛 + −14푛2 + −12 + −8푛 −14푛2 − − 12 14 Multiplying Multivariable Polynomials Find the product of the binomials: (2푦 − 푥)(푦 − 푥) 2푦 + 2푦 + −푥 + −푥 2푦2 + −2푥푦 + + (푥2) 푥2 − 3푥푦 + © Edgenuity, Inc. 6 Instruction Multiplying Monomials and Binomials Slide 16 Difference of Squares • Difference of squares: Multiply: −2푥 + 8 −2푥 − 8 푎 = −2푥 푎 + 푏 푎 − 푏 = 푏 = 8 푎2 − 푎푏 + 푎푏 − 푏2 ( )2 − ( )2 푎2 − 푏2 − 64 18 Perfect Square Trinomials ADDITION • Perfect square trinomial: (푎 + 푏)2 = (푎 + 푏)(푎 + 푏) = Example: Multiply: (7푥 + 2)(7푥 + 2) 푎 = 푏 = 2 (7푥)2 + 2 7푥 2 + (2)2 + 28푥 + 4 Perfect Square Trinomials SUBTRACTION • Perfect square trinomial: (푎 − 푏)2 = (푎 − 푏)(푎 − 푏) = Example: Multiply: 푔 − 10 2 푎 = 푏 = 10 ( )2 − 2 10 + (10)2 − 20푔 + 100 © Edgenuity, Inc. 7 Summary Multiplying Monomials and Binomials ? Lesson Question What does the product of polynomials look like? Answer Slide 2 Review: Key Concepts • Multiplying a by a binomial or binomial by a binomial can be done by using the distributive property, a table, or algebra tiles. • Special products: • Difference of squares: 푎 + 푏 푎 − 푏 = 푎2 − 푏2 • Perfect trinomials (푎 − 푏)2= 푎2 − 2푎푏 + 푏2 (푎 + 푏)2= 푎2 + 2푎푏 + 푏2 © Edgenuity, Inc. 8 Summary Multiplying Monomials and Binomials Use this space to write any questions or thoughts about this lesson. © Edgenuity, Inc. 9.