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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.3 Special Products Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1.

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Presentation on theme: "Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.3 Special Products Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1."— Presentation transcript:

1 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.3 Special Products Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

2 2

3 3 Special Products In this section we will use the distributive property to develop patterns that will allow us to multiply some special binomials quickly. We will find the product of two binomials using a method called FOIL. We will learn a formula for finding the square of a binomial sum. We will also learn formula for finding the product of the sum and difference of two terms.

4 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 4 Multiplying Polynomials - FOIL Using the FOIL Method to Multiply Binomials first outside inside last FOIL Product of First terms Product of Outside terms Product of Inside terms Product of Last terms

5 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 5 Multiplying Polynomials - FOILEXAMPLE SOLUTION Multiply Combine like terms Multiply FOIL first outside inside last

6 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 6 Multiply: (5x + 2)(x + 7) (5x + 2)(x + 7) = 5x·x + 5x·7 + 2·x + 2·7 =5x x + 2x +14 =5x x +14 Product of the first terms Product of the outside terms Product of the inside terms Product of the last terms FOIL FOIL MethodEXAMPLE

7 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 7 Multiply: (5x + 2)(x + 7) (5x + 2)(x + 7) = 5x·x + 5x·7 + 2·x + 2·7 =5x x + 2x +14 =5x x +14 Product of the first terms Product of the outside terms Product of the inside terms Product of the last terms FOIL FOIL MethodEXAMPLE

8 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 8 Objective #1: Example

9 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 9 Objective #1: Example

10 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 10 Objective #1: Example

11 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Objective #1: Example

12 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 12

13 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 13 (A + B)(A – B) = A 2 – B 2 The product of the sum and the difference of the same two terms is the square of the first term minus the square of the second term. Multiplying the Sum and Difference of Two Terms

14 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 14 Objective #2: Example

15 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 15 Objective #2: Example

16 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 16 Objective #2: Example

17 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 17 Objective #2: Example

18 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 18

19 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 19 (A + B) 2 = A 2 + 2AB + B 2 The square of a binomial sum is the first term squared plus two times the product of the terms plus the last term squared. The Square of a Binomial Sum

20 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 20 Multiplying Polynomials – Special FormulasEXAMPLE SOLUTION Multiply Use the special-product formula shown. + + = Product + +

21 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 21 Objective #3: Example

22 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 22 Objective #3: Example

23 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 23 Objective #3: Example

24 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 24 Objective #3: Example

25 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 25

26 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 26 (A – B) 2 = A 2 – 2AB + B 2 The square of a binomial difference is the first term squared minus two times the product of the terms plus the last term squared. The Square of a Binomial Difference

27 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 27 Multiplying Polynomials – Special FormulasEXAMPLE SOLUTION Multiply Use the special-product formula shown. – + = Product – +

28 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 28 Objective #4: Example

29 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 29 Objective #4: Example

30 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 30 Objective #4: Example

31 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 31 Objective #4: Example

32 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 32 Multiplying Polynomials – Special Formulas The Square of a Binomial Sum The Square of a Binomial Difference The Product of the Sum and Difference of Two Terms


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