1. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.2 Multiplying Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

2. 2

3. 3 When multiplying exponential expressions with the same base, add the exponents. Product Rule

4. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 4 Multiply x 3 ·x 5 Use the Product Rule. When multiplying exponential expressions with the same base, add the exponents. Product RuleEXAMPLE

5. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 5 Multiply 2 3 ·2 2 Note: We do not change the base! Product RuleEXAMPLE

6. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 6 Objective #1: Example

7. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 7 Objective #1: Example

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

11. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 The Power Rule When an exponential expression is raised to a power, multiply the exponents. Place the product of the exponents on the base and remove the parentheses. Power Rule for Exponents

12. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 12 Simplify: (x 2 ) 5 When an exponential expression is raised to a power, multiply the exponents. Power Rule for ExponentsEXAMPLE

13. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 13 Simplify: (3 4 ) 2 Note: We do not change the base! Power RuleEXAMPLE

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 When a product is raised to a power, raise each factor to the power. Products to Powers Rule for Exponents

20. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 20 Objective #3: Example

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

25. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 25 To multiply monomials with the same variable base, multiply the coefficients and then multiply the variables. Use the product rule for exponents to multiply the variables: Keep the variable and add the exponents. Multiplying Monomials

26. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 26 Multiply: (3x 2 )(5x 7 ) Multiply the coefficients and multiply the variables. Add the exponents. Simplify. Multiplying MonomialsEXAMPLE

27. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 27 Multiply: (3x 2 )(5x 7 ) Multiply the coefficients and multiply the variables. Add the exponents. Simplify. Multiplying MonomialsEXAMPLE

28. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 28 Multiplying PolynomialsEXAMPLE SOLUTION Multiply: Rearrange factors Multiply coefficients and add exponents Simplify

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

32. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 32 To multiply a monomial and a polynomial that is not a monomial, use the distributive property to multiply each term of the polynomial by the monomial. Multiplying a Monomial and a Polynomial

33. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 33 Multiplying PolynomialsEXAMPLE SOLUTION Multiply: Distribute Multiply coefficients and add exponents

34. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 34 Objective #5: Example

35. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 35 Objective #5: Example

36. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 36

37. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 37 To multiply two polynomials, m ultiply each term of one polynomial by each term of the other polynomial. Then combine like terms. Multiplying Polynomials

38. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 38 Objective #6: Example

39. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 39 Objective #6: Example