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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