Notes 12.1 multiplying polynomials

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  • Notes 12.1 multiplying polynomials

    1. 1. MultiplyingPolynomials
    2. 2. Table of ContentsSlide 3-4: Multiplying a Polynomial by a MonomialSlide 5-14: Practice Multiplying a Polynomial by aMonomialSlide 15: Multiplying Polynomials using thehorizontal and vertical methodsSlide 16: Multiplying Polynomials using the BoxMethodSlide 17-22: Practice Multiplying Polynomials
    3. 3. Multiply a Polynomial by a MonomialMultiply each terminside the parenthesis 2 ( 2 3x 2x − 7x + 5 )by the monomialoutside theparenthesis.The number of termsinside the parenthesiswill be the same asafter multiplying.
    4. 4. Multiply a Polynomial by a MonomialMultiply each terminside the parenthesis 2 ( 3x 2x − 7x + 52 )by the monomialoutside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2parenthesis.The number of termsinside the parenthesiswill be the same asafter multiplying.
    5. 5. Multiply a Polynomial by a MonomialMultiply each terminside the parenthesis 2 ( 3x 2x − 7x + 52 )by the monomialoutside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2parenthesis.The number of termsinside the parenthesiswill be the same asafter multiplying.
    6. 6. Multiply a Polynomial by a MonomialMultiply each terminside the parenthesis 2 ( 3x 2x − 7x + 52 )by the monomialoutside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2parenthesis.The number of termsinside the parenthesis 2 ( 3x 2x − 7x + 5 2 )will be the same asafter multiplying.
    7. 7. Multiply a Polynomial by a MonomialMultiply each terminside the parenthesis 2 ( 3x 2x − 7x + 52 )by the monomialoutside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2parenthesis.The number of termsinside the parenthesis 2 ( 3x 2x − 7x + 5 2 )will be the same as 4 6x − 21x + 15x 3 2after multiplying.
    8. 8. Multiply a Polynomial by a MonomialReview this Cool Math site to learn aboutmultiplying a polynomial by a monomial.Do the Try It and Your Turn problems inyour notebook and check your answers onthe next slides.
    9. 9. Cool Math Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 )
    10. 10. Cool Math Try It - Page 1 Multiply: 4 ( 6x 2x + 32 )Distribute the monomial.
    11. 11. Cool Math Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 )Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3
    12. 12. Cool Math Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 )Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3 Multiply each term.
    13. 13. Cool Math Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 )Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3 Multiply each term. 6 4 12x + 18x
    14. 14. Cool Math Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 )Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3 Multiply each term. 6 4 12x + 18x Verify that your answer has same number of terms as inside original ( ). Both have 2 terms.
    15. 15. What is the degree of the previous answer? 6 4 12x + 18x
    16. 16. What is the degree of the previous answer? 6 4 12x + 18xFirst term is degree 6.
    17. 17. What is the degree of the previous answer? 6 4 12x + 18xFirst term is degree 6.Second term is degree 4.
    18. 18. What is the degree of the previous answer? 6 4 12x + 18xFirst term is degree 6.Second term is degree 4.Therefore, the polynomial is degree 6.
    19. 19. Your Turn - Page 2 multiply:
    20. 20. Your Turn - Page 2 multiply: 3 ( 5 2 10x 2x + 1 − 3x + x )
    21. 21. Your Turn - Page 2 multiply: 3 ( 5 2 10x 2x + 1 − 3x + x )Distribute the monomial.
    22. 22. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 − 3x + x5 2 )Distribute the monomial. ( ) 10x 2x + 10x (1) + 10x −3x + 10x ( x ) 3 5 3 3 ( 2 ) 3
    23. 23. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 − 3x + x5 2 ) ( ) 10x 2x + 10x (1) + 10x −3x + 10x ( x ) 3 5 3 3 ( 2 ) 3Multiply each term.
    24. 24. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 − 3x + x 5 2 ) ( ) 10x 2x + 10x (1) + 10x −3x + 10x ( x ) 3 5 3 3 ( 2 ) 3Multiply each term. 8 3 5 4 20x + 10x − 30x + 10x
    25. 25. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 − 3x + x 5 2 ) ( ) 10x 2x + 10x (1) + 10x −3x + 10x ( x ) 3 5 3 3 ( 2 ) 3 8 3 5 4 Put in descending 20x + 10x − 30x + 10x order and verify number of terms.(Both have 4 terms.)
    26. 26. Your Turn - Page 2 multiply: 3 ( 10x 2x + 1 − 3x + x 5 2 ) ( ) 10x 2x + 10x (1) + 10x −3x + 10x ( x ) 3 5 3 3 ( 2 ) 3 8 3 5 4 Put in descending 20x + 10x − 30x + 10x order and verify number of terms. 8 5 4 3(Both have 4 terms.) 20x − 30x + 10x + 10x
    27. 27. What is the degree of the previous answer? 8 5 4 3 20x − 30x + 10x + 10x
    28. 28. What is the degree of the previous answer? 8 5 4 3 20x − 30x + 10x + 10xFirst term is degree 8.
    29. 29. What is the degree of the previous answer? 8 5 4 3 20x − 30x + 10x + 10xFirst term is degree 8.Second term is degree 5.
    30. 30. What is the degree of the previous answer? 8 5 4 3 20x − 30x + 10x + 10xFirst term is degree 8.Second term is degree 5.Third term is degree 4.
    31. 31. What is the degree of the previous answer? 8 5 4 3 20x − 30x + 10x + 10xFirst term is degree 8.Second term is degree 5.Third term is degree 4.Fourth term is degree 3.
    32. 32. What is the degree of the previous answer? 8 5 4 3 20x − 30x + 10x + 10xFirst term is degree 8.Second term is degree 5.Third term is degree 4.Fourth term is degree 3.Therefore, the polynomial is degree 8.
    33. 33. Try It - Page 2 Multiply: 2 5 ( 2 2 4 4x w w − x + 6xw − 1 + 3x w 8 )
    34. 34. Try It - Page 2 Multiply: 2 5 ( 2 2 4 4x w w − x + 6xw − 1 + 3x w 8 )Distribute the monomial.
    35. 35. Try It - Page 2 Multiply: 2 5 ( 4x w w − x + 6xw − 1 + 3x w 2 2 4 8 )Distribute the monomial. 5 ( 2 ) 2 5 ( 2 ) 4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w 2 5 2 2 5 2 5 ( 4 8 )
    36. 36. Try It - Page 2 Multiply: 2 5 ( 4x w w − x + 6xw − 1 + 3x w 2 2 4 8 ) 5 ( 2 ) 2 5 ( 2 )4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w 2 5 2 2 5 2 5 ( 4 8 )Multiply each term.
    37. 37. Try It - Page 2 Multiply: 2 5 ( 4x w w − x + 6xw − 1 + 3x w 2 2 4 8 ) 5 ( 2 )4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w 2 5 2 2 5 ( 2 ) 2 5 2 5 ( 4 8 )Multiply each term. 2 6 4 5 3 7 2 5 6 13 4x w − 4x w + 24x w − 4x w + 12x wVerify answer has 5 terms like original parenthesis.
    38. 38. What is the degree of the previous answer? 2 6 4 5 3 7 2 5 6 134x w − 4x w + 24x w − 4x w + 12x w
    39. 39. What is the degree of the previous answer? 2 6 4 5 3 7 2 5 6 134x w − 4x w + 24x w − 4x w + 12x wFirst term is degree 8.
    40. 40. What is the degree of the previous answer? 2 6 4 5 3 7 2 5 6 134x w − 4x w + 24x w − 4x w + 12x wFirst term is degree 8.Second term is degree 9.
    41. 41. What is the degree of the previous answer? 2 6 4 5 3 7 2 5 6 134x w − 4x w + 24x w − 4x w + 12x wFirst term is degree 8.Second term is degree 9.Third term is degree 10.
    42. 42. What is the degree of the previous answer? 2 6 4 5 3 7 2 5 6 134x w − 4x w + 24x w − 4x w + 12x wFirst term is degree 8.Second term is degree 9.Third term is degree 10.Fourth term is degree 7.
    43. 43. What is the degree of the previous answer? 2 6 4 5 3 7 2 5 6 134x w − 4x w + 24x w − 4x w + 12x wFirst term is degree 8.Second term is degree 9.Third term is degree 10.Fourth term is degree 7.Fifth term is degree 19.
    44. 44. What is the degree of the previous answer? 2 6 4 5 3 7 2 5 6 134x w − 4x w + 24x w − 4x w + 12x wFirst term is degree 8.Second term is degree 9.Third term is degree 10.Fourth term is degree 7.Fifth term is degree 19.Therefore, the polynomial is degree 19.
    45. 45. Try this one... Multiply: ( 2 3x 2x − 5x + 7 )
    46. 46. Try this one... Multiply: ( 2 3x 2x − 5x + 7 )Distribute the monomial.
    47. 47. Try this one... Multiply: ( 2 3x 2x − 5x + 7 )Distribute the monomial. ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2
    48. 48. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2Multiply each term.
    49. 49. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2Multiply each term. 3 2 6x − 15x + 21x
    50. 50. What is the degree of the previous answer? 3 2 6x − 15x + 21x
    51. 51. What is the degree of the previous answer? 3 2 6x − 15x + 21xFirst term is degree 3.
    52. 52. What is the degree of the previous answer? 3 2 6x − 15x + 21xFirst term is degree 3.Second term is degree 2.
    53. 53. What is the degree of the previous answer? 3 2 6x − 15x + 21xFirst term is degree 3.Second term is degree 2.Third term is degree 1.
    54. 54. What is the degree of the previous answer? 3 2 6x − 15x + 21xFirst term is degree 3.Second term is degree 2.Third term is degree 1.Therefore, the polynomial is degree 3.
    55. 55. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b2 3 5 )
    56. 56. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 2 3 5 )Distribute the monomial.
    57. 57. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 2 3 5 )Distribute the monomial. ( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b ) 2 2 3 2 2 2 3 2 2 5
    58. 58. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 2 3 5 )( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b ) 2 2 3 2 2 2 3 2 2 5Multiply each term.
    59. 59. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 2 3 5 )( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b ) 2 2 3 2 2 2 3 2 2 5Multiply each term. 5 2 4 5 2 7 −2a b − 6a b + 8a b
    60. 60. What is the degree of the previous answer? 5 2 4 5 2 7 −2a b − 6a b + 8a b
    61. 61. What is the degree of the previous answer? 5 2 4 5 2 7 −2a b − 6a b + 8a bFirst term is degree 7.
    62. 62. What is the degree of the previous answer? 5 2 4 5 2 7 −2a b − 6a b + 8a bFirst term is degree 7.Second term is degree 9.
    63. 63. What is the degree of the previous answer? 5 2 4 5 2 7 −2a b − 6a b + 8a bFirst term is degree 7.Second term is degree 9.Third term is degree 9.
    64. 64. What is the degree of the previous answer? 5 2 4 5 2 7 −2a b − 6a b + 8a bFirst term is degree 7.Second term is degree 9.Third term is degree 9.Therefore, the polynomial is degree 9.
    65. 65. Multiplying PolynomialsWatch this 6 minute video to learn how to multiply atrinomial by a binomial.Here’s the link to copy/paste if the hyperlink didn’t work: http://www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-270s.htmlThe video shows you 2 methods, the horizontal methodand vertical method.Alternative: Visit the PurpleMath website to learn howto multiply polynomials using these methods.The next slide will show you another method formultiplying polynomials, called the box method.
    66. 66. Box methodThe previous video showed you how tomultiply 2 polynomials, which can get messy.The Box Method is a way to keep youorganized while multiplying.Follow this link to see a 5 minute videoorganizing the multiplication using boxes.Here’s the link to copy/paste if the hyperlink doesn’t work: http://www.slideshare.net/secret/iiYvYrvk1SxdrG
    67. 67. Practice Multiplying 2 Binomials You’ve seen 3 different methods for multiplying polynomial: 1) Horizontal Method; 2) Vertical Method; 3) Box Method Practice your favorite method at Coolmath. Select the “Give me a Problem” button to keep trying problems. Do your work in a notebook. When you select “What’s the Answer?” your answer is erased and correct answer is displayed. Having your work in a notebook will allow you to compare your answer to the correct answer. Keep working problems until you get 4 out of 5 correct. The next 2 slides show multiplying 2 binomials using the box method.
    68. 68. Example: ( 5x + 8 ) ( 3x − 1)
    69. 69. Example: ( 5x + 8 ) ( 3x − 1) 3x −15x8
    70. 70. Example: ( 5x + 8 ) ( 3x − 1) 3x −15x 15x 2 5x8 24x −8
    71. 71. Example: ( 5x + 8 ) ( 3x − 1) 2 3x −1 = 15x + 29x − 85x 15x 2 5x8 24x −8
    72. 72. Example: ( 4n − 3) ( 3n − 2 )
    73. 73. Example: ( 4n − 3) ( 3n − 2 ) 3n −24n−3
    74. 74. Example: ( 4n − 3) ( 3n − 2 ) 3n −24n 12n 2 −8n−3 −9n 6
    75. 75. Example: ( 4n − 3) ( 3n − 2 ) 2 3n −2 = 12n − 17n + 64n 12n 2 −8n−3 −9n 6
    76. 76. Practice Multiplying 2 Polynomials Now that you are an EXPERT at the easy problems, try some harder problems at Coolmath. If you have trouble, go back and review a method. Remember, you can also see me on Pronto! Select the “Give me a Problem” button to keep trying problems. Do your work in a notebook. When you select “What’s the Answer?” your answer is erased and correct answer is displayed. Having your work in a notebook will allow you to compare your answer to the correct answer. Keep working problems until you get 4 out of 5 correct. The next 2 slides show multiplying 2 polynomials using the box method.
    77. 77. Example: ( 4k + 3k + 9 ) ( k + 3) 2
    78. 78. Example: ( 4k + 3k + 9 ) ( k + 3) 2 2 4k 3k 9k3
    79. 79. Example: ( 4k + 3k + 9 ) ( k + 3) 2 2 4k 3k 9k 3 2 4k 3k 9k3 12k 2 9k 27
    80. 80. Example: ( 4k + 3k + 9 ) ( k + 3) 2 2 4k 3k 9k 3 2 4k 3k 9k3 12k 2 9k 27 3 2 = 4k + 15k + 18k + 27
    81. 81. Example: ( 2x − 3) ( 3x − 5x + 7 ) 2
    82. 82. Example: ( 2x − 3) ( 3x − 5x + 7 ) 2 2 3x −5x 72x−3
    83. 83. Example: ( 2x − 3) ( 3x − 5x + 7 ) 2 2 3x −5x 72x 3 2 6x −10x 14x−3 −9x 2 15x −27
    84. 84. Example: ( 2x − 3) ( 3x − 5x + 7 ) 2 2 3x −5x 72x 3 2 6x −10x 14x−3 −9x 2 15x −27 3 2 = 6x − 19x + 29x − 27
    85. 85. Extra HelpHere’s a cool site. Enter the polynomialsyou wish to multiply and it gives you theanswer. A description of how to multiplythe polynomials is included.If the above hyperlink doesn’t work, copy/paste this link: http://www.webmath.com/polymult.html
    86. 86. FANTASTIC job! You areready to Master theAssignment. Good Luck!

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