2. ESSENTIAL QUESTION
• How do you multiply polynomials by monomials?
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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