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Int Math 2 Section 9-4 1011

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Jimbo Lamb

This document provides examples for multiplying polynomials by monomials. It begins with an essential question about multiplying polynomials by monomials and where this concept is applied. It then provides 4 examples of simplifying polynomial multiplication, showing the step-by-step work. It concludes with an example problem involving writing and simplifying expressions for the areas of different figures.

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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 job, sports, finance, geography
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 )
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 )
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 )
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 )
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 )
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 )
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 )
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 )
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 )
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 )
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
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
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
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
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
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
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
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
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
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
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
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
EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2
EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 4h(6h +1)
EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2 4h(6h +1)
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
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
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
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
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
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
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
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
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
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
PROBLEM SET
PROBLEM SET p. 392 #1-54 multiples of 3 “A candle loses none of its light by lighting another candle.” - Unknown

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Int Math 2 Section 9-4 1011

  • 1. SECTION 9-4 Multiply a Polynomial by a Monomial
  • 2. ESSENTIAL QUESTION • How do you multiply polynomials by monomials? • Where you’ll see this: • Travel, part-time job, sports, finance, geography
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. EXAMPLE 2 Write and simplify an expression for the area of each figure. a. 4h b. 3x2 + 2 6h + 1 2x2
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
  • 39. PROBLEM SET p. 392 #1-54 multiples of 3 “A candle loses none of its light by lighting another candle.” - Unknown

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