Multiplying
Polynomials
Module 9 - Topic 2
     Part 1
Multiply a Polynomial by a
            Monomial
Multiply each term
inside the parenthesis
                           2
   ...
Multiply a Polynomial by a
            Monomial
Multiply each term
inside the parenthesis
                                ...
Multiply a Polynomial by a
            Monomial
Multiply each term
inside the parenthesis
                                ...
Multiply a Polynomial by a
            Monomial
Multiply each term
inside the parenthesis
                                ...
Multiply a Polynomial by a
            Monomial
Multiply each term
inside the parenthesis
                                ...
Multiply a Polynomial by a
           Monomial
Review this Cool Math site to learn about
multiplying a polynomial by a mon...
Try It - Page 1
 Multiply:         4
                       (
                  6x 2x + 32
                               )
Try It - Page 1
    Multiply:               4
                                (
                           6x 2x + 32
    ...
Try It - Page 1
    Multiply:                    4
                                     (
                             6x ...
Try It - Page 1
    Multiply:                    4
                                     (
                             6x ...
Try It - Page 1
    Multiply:                    4
                                     (
                             6x ...
Try It - Page 1
    Multiply:                    4
                                     (
                             6x ...
Your Turn - Page 2
 multiply:
Your Turn - Page 2
 multiply:
                3
                    (   5   2
             10x 2x + 1 − 3x + x   )
Your Turn - Page 2
    multiply:
                              3
                                  (   5   2
             ...
Your Turn - Page 2
    multiply:
                              3
                                  (
                     ...
Your Turn - Page 2
    multiply:
                             3
                                 (
                       ...
Your Turn - Page 2
    multiply:
                                 3
                                     (
               ...
Your Turn - Page 2
     multiply:
                                  3
                                      (
            ...
Your Turn - Page 2
     multiply:
                                      3
                                          (
    ...
Try It - Page 2
 Multiply:
               2   5
                       (   2   2     4
             4x w w − x + 6xw − 1 +...
Try It - Page 2
      Multiply:
                           2   5
                                   (   2   2   4
        ...
Try It - Page 2
       Multiply:
                                  2       5
                                             ...
Try It - Page 2
      Multiply:
                                2       5
                                            (
  ...
Try It - Page 2
      Multiply:
                                              2       5
                                  ...
Try this one...
 Multiply:          (   2
                  3x 2x − 5x + 7   )
Try this one...
    Multiply:                (   2
                           3x 2x − 5x + 7   )
Distribute the monomial.
Try this one...
    Multiply:                    (   2
                               3x 2x − 5x + 7   )
Distribute the mo...
Try this one...
   Multiply:                 (   2
                           3x 2x − 5x + 7   )

                      ( ...
Try this one...
   Multiply:                 (   2
                           3x 2x − 5x + 7   )

                      ( ...
Try this one...
 Multiply:        2 2
                        (   3
             −2a b a + 3a b − 4b2   3   5
            ...
Try this one...
    Multiply:              2 2
                                 (   3
                     −2a b a + 3a b ...
Try this one...
    Multiply:                2 2
                                   (   3
                      −2a b a + ...
Try this one...
   Multiply:                2 2
                                  (   3
                      −2a b a + 3a...
Try this one...
   Multiply:                 2 2
                                   (   3
                      −2a b a + ...
Great job working
all those problems!

Proceed to Part 2.
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Module 9 Topic 2 multiplying polynomials - part 1

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  • Module 9 Topic 2 multiplying polynomials - part 1

    1. 1. Multiplying Polynomials Module 9 - Topic 2 Part 1
    2. 2. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 2 3x 2x − 7x + 5 ) by the monomial outside the parenthesis. The number of terms inside the parenthesis will be the same as after multiplying.
    3. 3. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 3x 2x − 7x + 52 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis will be the same as after multiplying.
    4. 4. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 3x 2x − 7x + 52 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis will be the same as after multiplying.
    5. 5. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 3x 2x − 7x + 52 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis 2 ( 3x 2x − 7x + 5 2 ) will be the same as after multiplying.
    6. 6. Multiply a Polynomial by a Monomial Multiply each term inside the parenthesis 2 ( 3x 2x − 7x + 52 ) by the monomial outside the 3x 2 ( 2x ) + 3x ( −7x ) + 3x ( 5 ) 2 2 2 parenthesis. The number of terms inside the parenthesis 2 ( 3x 2x − 7x + 5 2 ) will be the same as 4 6x − 21x + 15x 3 2 after multiplying.
    7. 7. Multiply a Polynomial by a Monomial Review this Cool Math site to learn about multiplying a polynomial by a monomial. Do the Try It and Your Turn problems in your notebook and check your answers on the next slides.
    8. 8. Try It - Page 1 Multiply: 4 ( 6x 2x + 32 )
    9. 9. Try It - Page 1 Multiply: 4 ( 6x 2x + 32 ) Distribute the monomial.
    10. 10. Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 ) Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3
    11. 11. Try It - Page 1 Multiply: 4 ( 6x 2x + 3 2 ) Distribute the monomial. 4 2 4 6x ⋅ 2x + 6x ⋅ 3 Multiply each term.
    12. 12. 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
    13. 13. 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 your answer has same number of terms as inside original ( ). Both have 2 terms.
    14. 14. Your Turn - Page 2 multiply:
    15. 15. Your Turn - Page 2 multiply: 3 ( 5 2 10x 2x + 1 − 3x + x )
    16. 16. Your Turn - Page 2 multiply: 3 ( 5 2 10x 2x + 1 − 3x + x ) Distribute the monomial.
    17. 17. 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
    18. 18. 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 ) 3 Multiply each term.
    19. 19. 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 Multiply each term. 8 3 5 4 20x + 10x − 30x + 10x
    20. 20. 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.)
    21. 21. 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
    22. 22. Try It - Page 2 Multiply: 2 5 ( 2 2 4 4x w w − x + 6xw − 1 + 3x w 8 )
    23. 23. Try It - Page 2 Multiply: 2 5 ( 2 2 4 4x w w − x + 6xw − 1 + 3x w 8 ) Distribute the monomial.
    24. 24. 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 )
    25. 25. 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.
    26. 26. 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 w Verify answer has 5 terms like original parenthesis.
    27. 27. Try this one... Multiply: ( 2 3x 2x − 5x + 7 )
    28. 28. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) Distribute the monomial.
    29. 29. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) Distribute the monomial. ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2
    30. 30. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2 Multiply each term.
    31. 31. Try this one... Multiply: ( 2 3x 2x − 5x + 7 ) ( ) 3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 ) 2 Multiply each term. 3 2 6x − 15x + 21x
    32. 32. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b2 3 5 )
    33. 33. Try this one... Multiply: 2 2 ( 3 −2a b a + 3a b − 4b 2 3 5 ) Distribute the monomial.
    34. 34. 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
    35. 35. 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 5 Multiply each term.
    36. 36. 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 5 Multiply each term. 5 2 4 5 2 7 −2a b − 6a b + 8a b
    37. 37. Great job working all those problems! Proceed to Part 2.

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