Multiplying Polynomials MATH 017 Intermediate Algebra S. Rook.

Slides:

Advertisements

Similar presentations

Multiplying Polynomials

Advertisements

Section P4 Polynomials. How We Describe Polynomials.

Two Similar Approaches Basic Distributive Property

Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 + 7y – 8y 2 – 1 ANSWER 2y 2 + 7y – 1.

Chapter 5 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

4.5 Multiplying Polynomials

Multiplication of Polynomials.  Use the Distributive Property when indicated.  Remember: when multiplying 2 powers that have like bases, we ADD their.

§ 4.5 Multiplication of Polynomials. Angel, Elementary Algebra, 7ed 2 Multiplying Polynomials To multiply a monomial by a monomial, multiply their coefficients.

Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook.

Adding and Subtracting Polynomials Section 0.3. Polynomial A polynomial in x is an algebraic expression of the form: The degree of the polynomial is n.

Multiplying & Dividing Rational Expressions MATH 018 Combined Algebra S. Rook.

Rational Exponents MATH 017 Intermediate Algebra S. Rook.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.

MULTIPLICATION OF POLYNOMIALS CHAPTER 4 SECTION 5 MTH Algebra.

Simplifying Rational Expressions MATH 018 Combined Algebra S. Rook.

Dividing Polynomials MATH 017 Intermediate Algebra S. Rook.

1.2 - Products Commutative Properties Addition: Multiplication:

6.4 M ULTIPLYING P OLYNOMIALS Sec Copyright © 2010 Pearson Education, Inc. All rights reserved. Multiplying Monomials We multiply polynomials by.

Factoring Easy and Hard Trinomials MATH 017 Intermediate Algebra S. Rook.

Warm Up Simplify each expression: 1.(-4) (5x) 2 5x 1 4.-(-4.9) 0 5.[(3x 4 y 7 z 12 ) 5 (–5x 9 y 3 z 4 ) 2 ] 0.

Bell Work 11/22. Homework Due 11/25 Exponents & Exponential Functions Page 82 #1-28 all.

Chapter 5 Section 5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson.

C HAPTER 10 – P OLYNOMIALS AND FACTORING 10.2 – Multiplying Polynomials.

Objective The student will be able to: multiply two polynomials using the FOIL method, Box method and the distributive property.

Review Operations with Polynomials December 9, 2010.

5.4 Multiplying Polynomials

Multiplying Polynomials *You must know how to multiply before you can factor!”

Aim: How do we multiply polynomials? Do Now: Multiply the following 1. 2x(3x + 1) 2. (x – 1)(x + 2) 3. (x +2)(x 2 – 3x + 1)

Day Problems Simplify each product. 1. 8m(m + 6) 2. -2x(6x3 – x2 + 5x)

Ch 10: Polynomials B) Multiplying Objective: To multiply polynomials using various techniques.

Essential Question. Daily Standard & Essential Question MM1A2c:Add, subtract, multiply, and divide polynomials MM1A2g: use area and volume models for.

Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 1 Exponents and Polynomials 5.

5.9 Multiplication of Monomials and Binomials Goals: 1.To multiply a monomial and a poly 2.To multiply 2 binomials (FOIL)

Adding & Subtracting Polynomials MATH 018 Combined Algebra S. Rook.

Using Distribution with Polynomials Copyright Scott Storla 2015.

Absolute Value Equations MATH 017 Intermediate Algebra S. Rook.

Polynomials Lesson 5.2: Adding, Subtracting, and Multiplying Polynomials By: Just Just Leininger Period 3 modern algebra.

Binomial X Binomial The problems will look like this: (x – 4)(x + 9)

Multiplying Polynomials Section Multiplying Monomials To multiply two monomials use the associative and commutative properties and regroup. Remember.

§ 5.4 Special Products. Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 The FOIL Method When multiplying two binomials, the distributive property.

1.(-7) (-2) 2.(3)(-6) 3.(4)(5) 4.(-3) (4t) 5.(2)(-2x) 6.(7y)(3) 7.3(s+5) 8.4(-n+2) 9.4-(t+2) 10.3n+(2-n) Algebra S9 Day 21.

5.9 Multiplication of Monomials and Binomials How to Multiply a Mono by a Poly: Distribute the monomial by the polynomial.

ADD & SUBTRACT POLYNOMIALS. 1. Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms. 9y - 3y - 7x + 8x + 15a - 8a 6y.

Lesson 10.2 Multiplying Polynomials Objective: To multiply polynomials Multiply monomials by other polynomials by using distributive property Examples.

Objective The student will be able to: multiply two polynomials using the distributive property.

Adding and Subtracting Rational Expressions MATH 017 Intermediate Algebra S. Rook.

1.4 Polynomials. Polynomials Degree of term = sum of exponents on variables Degree of Poly = largest degree among terms Poly Type (# of terms) Degree.

Multiply two binomials using FOIL method

In this lesson, we will multiply polynomials

Section 9.3 – 9.4 Review Algebra I.

Multiplication of monomial and binomials.

Polynomials and Polynomial Functions

Aim: What are the product and power rules of exponents?

7.8 Multiplying Polynomials

Bell Work 3/26/2015 Simplify..

13 Exponents and Polynomials.

8-2 Multiplying and Factoring

MULTIPLYING BINOMIALS

Problem of the Day (4x2 – 2x – 6) + (4x2 – 7x + 10)

Objective multiply two polynomials using the FOIL method and the distributive property.

Multiplication of Polynomials

Unit 1 Section 3B: MULTIPLYING POLYNOMIALS

Section P4 Polynomials.

(B12) Multiplying Polynomials

(2)(4) + (2)(5) + (3)(4) + (3)(5) =

Warm Up Simplify the expression by using distributive property and then combining like terms. x(x + 5) + 4(x + 5)

Multiplying Polynomials

5.10 Multiplying Binomials: Special Products

9.2 Multiplying Polynomials fguilbert.

Presentation transcript:

Multiplying Polynomials MATH 017 Intermediate Algebra S. Rook

2 Overview Section 5.4 in the textbook –Multiply by monomials –Multiply binomials –Square binomials –Multiply (a + b)(a – b) –Multiply more than two polynomials

Multiplying by a Monomial

4 Use the distributive property Simplify using exponent rules

5 Multiplying by a Monomial (Example) Ex 1: Multiply:

6 Multiplying by a Monomial (Example) Ex 2: Multiply:

Multiply Binomials

8 Multiplying Polynomials in General To multiply (4x + 3)(2x 2 – 3x + 7), we use the distributive property = 4x(2x 2 – 3x + 7) + 3(2x 2 – 3x + 7) Simplify and combine any like terms

9 Multiplying Polynomials in General (Example) Ex 3: Multiply (3x 2 + 4x – 5)(3x + 2)

10 Multiplying Binomials Recall that a binomial is a polynomial with 2 terms Can also use the distributive property A helpful pneumonic is FOIL (essentially the distributive property) F irst O uter I nner L ast

11 Multiplying Binomials (Example) Ex 4: Multiply: (4x + 5)(3x - 2)

12 Multiplying Binomials (Example) Ex 5: Multiply: (2x - 7)(x - 8)

Square Binomials

14 Square Binomials First expand: (a + b) 2 = (a + b)(a + b) Finally use FOIL Do NOT just square each of the individual terms! (a + b) 2 ≠ a 2 + b 2

15 Square Binomials (Example) Ex 6: Multiply: (3x + 2y) 2

16 Square Binomials (Example) Ex 7: Multiply: (4x – 5) 2

Multiply (a + b)(a – b)

18 Multiply (a + b)(a – b) A special product Use FOIL to simplify The O and the I terms cancel

19 Multiply (a + b)(a – b) (Example) Ex 8: Multiply (m – 3n)(m + 3n)

20 Multiply (a + b)(a – b) (Example) Ex 9: Multiply (2r 4 + 5s 2 )(2r 4 – 5s 2 )

Multiply More than Two Polynomials

22 Multiply More than Two Polynomials Multiply the first two polynomials using the techniques discussed thus far Use the distributive property to multiply the result by the last polynomial Simplify

23 Multiply More than Two Polynomials (Example) Ex 10: Multiply (x + 2)(x – 7)(x + 1)

24 Multiply More than Two Polynomials (Example) Ex 11: Multiply (x + 4) 2 (7x – 2)

25 Summary After studying these slides, you should know how to do the following: –Multiply by monomials –Multiply binomials –Square binomials –Multiply (a + b)(a – b) –Multiply more than two polynomials