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SECTION 9-4
Multiply a Polynomial by a Monomial
ESSENTIAL QUESTION


• How   do you multiply polynomials by monomials?



• Where   you’ll see this:

 • Travel, part-time...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                              2
                               ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                              2
                               ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                              2
                               ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                              2
                               ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                              2
                               ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                              2
                               ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                    2
                         ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                    2
                         ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                 2
                            ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                 2
                            ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                 2
                            ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                 2
                            ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                 2
                            ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                 2
                            ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                 2
                            ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                 2
                            ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                   2
                          ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                   2
                          ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                    2
                         ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                    2
                         ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                    2
                         ...
EXAMPLE 1
                       Simplify.
   a. 2x(2x + y)                                    2
                         ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.      4h                  b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.      4h                  b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.      4h                  b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.             4h            b.
                  ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.             4h            b.
                  ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.        4h                b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.        4h                b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.        4h                b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.        4h                b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.        4h                b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.        4h                b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.        4h                b.
                   ...
EXAMPLE 2
Write and simplify an expression for the area of each figure.
 a.        4h                b.
                   ...
HOMEWORK
HOMEWORK


                p. 392 #1-54 multiples of 3




“A candle loses none of its light by lighting another candle.”
...
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Integrated Math 2 Section 9-4

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Multiply a Polynomial by a Monomial

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Integrated Math 2 Section 9-4

  1. 1. SECTION 9-4 Multiply a Polynomial by a Monomial
  2. 2. ESSENTIAL QUESTION • How do you multiply polynomials by monomials? • Where you’ll see this: • Travel, part-time job, sports, finance, geography
  3. 3. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  4. 4. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  5. 5. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 4x 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  6. 6. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 4x 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  7. 7. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 4x +2xy 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  8. 8. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 4x +2xy 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  9. 9. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 4x +2xy 10w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  10. 10. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 4x +2xy 10w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  11. 11. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  12. 12. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y )
  13. 13. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 −6n
  14. 14. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 −6n
  15. 15. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 2 −6n −8n
  16. 16. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 2 −6n −8n
  17. 17. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 2 −6n −8n +10n
  18. 18. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 2 −6n −8n +10n
  19. 19. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 3 3 −6n −8n +10n2 10x y
  20. 20. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 3 3 −6n −8n +10n2 10x y
  21. 21. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 3 2 5 3 −6n −8n +10n2 10x y +30x y
  22. 22. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 3 2 5 3 −6n −8n +10n2 10x y +30x y
  23. 23. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 3 2 5 4 4 3 −6n −8n +10n2 10x y +30x y +15x y
  24. 24. EXAMPLE 1 Simplify. a. 2x(2x + y) 2 b. − 5w(−2w + 4w ) 2 3 2 4x +2xy 10w −20w 2 2 2 3 2 2 c. − 2n(3n + 4n − 5) d. 5x y (2xy + 6y + 3x y ) 3 3 2 5 4 4 3 −6n −8n +10n2 10x y +30x y +15x y 4 4 3 3 2 5 15x y +10x y + 30x y
  25. 25. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2
  26. 26. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 4h(6h +1)
  27. 27. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 4h(6h +1)
  28. 28. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 4h(6h +1) 2 24h
  29. 29. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 4h(6h +1) 2 24h
  30. 30. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 4h(6h +1) 2 24h +4h
  31. 31. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 4h(6h +1) 24h 2 +4h units2
  32. 32. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 2 2 4h(6h +1) 2x (3x + 2) 24h 2 +4h units2
  33. 33. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 2 2 4h(6h +1) 2x (3x + 2) 24h 2 +4h units2
  34. 34. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 2 2 4h(6h +1) 2x (3x + 2) 4 24h 2 +4h units2 6x
  35. 35. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 2 2 4h(6h +1) 2x (3x + 2) 4 24h 2 +4h units2 6x
  36. 36. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 2 2 4h(6h +1) 2x (3x + 2) 4 2 24h 2 +4h units2 6x +4x
  37. 37. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 2 2 4h(6h +1) 2x (3x + 2) 4 2 24h 2 +4h units2 6x +4x units2
  38. 38. HOMEWORK
  39. 39. HOMEWORK p. 392 #1-54 multiples of 3 “A candle loses none of its light by lighting another candle.” - Unknown

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