Multiply a Polynomial by a Monomial

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

38. PROBLEM SET

39. PROBLEM SET
p. 392 #1-54 multiples of 3
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