1. 9.2 - Multiplying Polynomials
Do NOW
Is this expression a polynomial? If so, write it in standard form and determine its highest degree, type, leading coefficient, and constant term.
x3 + 4x2 + 8
x3 + x4y2 + x–2
Find the sum or difference
3) (3x2 – 2x + 9) + (x2 + 2x – 4)
4) (–4x2 + 3x – 1) – (x2 + 2x – 6)
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9.2 - Multiplying Polynomials

2. 9.2 - Multiplying Polynomials
Worksheet Key
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9.2 - Multiplying Polynomials

3. Multiplying of Polynomials
Section 9.2
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9.2 - Multiplying Polynomials

4. Multiplying Monomials
Any term that is considered ONE term
If the variable has two bases, think, BASE, BASE, ADD. [add the bases]
If the variables have power upon power, think, POWER, POWER, MULTIPLY [multiply the powers]
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9.2 - Multiplying Polynomials

5. 9.2 - Multiplying Polynomials
Example 1
Multiply (5x3) (4x5)
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9.2 - Multiplying Polynomials

6. 9.2 - Multiplying Polynomials
Example 2
Multiply (5x2y3)3
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9.2 - Multiplying Polynomials

7. 9.2 - Multiplying Polynomials
Example 3
Multiply (–2x3y)4
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9.2 - Multiplying Polynomials

8. 9.2 - Multiplying Polynomials
Your Turn
Multiply (–3a4bc2)3
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9.2 - Multiplying Polynomials

9. 9.2 - Multiplying Polynomials
Example 4
Multiply 5x(2x3 + 6)
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9.2 - Multiplying Polynomials

10. 9.2 - Multiplying Polynomials
Example 5
Multiply –3x2(5x2 + 6x – 1)
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9.2 - Multiplying Polynomials

11. 9.2 - Multiplying Polynomials
Your Turn
Multiply –5x3(2x2 – 9x + 2)
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9.2 - Multiplying Polynomials

12. Multiplying Binomials
FOIL Method:
FIRST: Multiply the first term in the first bracket and first term in the second bracket
OUTER: Multiply the first term in the first bracket and second term in the second bracket
INNER: Multiply the second term in the first bracket and first term in the second bracket
LAST: Multiply the second term in the first bracket and second term in the second bracket
Simplify the expression by combining like terms
Check using your graphing calculator by looking at the graph and at y1 = y2
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9.2 - Multiplying Polynomials

13. Multiplying Binomials
Box Method:
Create a 2x2 box with each factor going on top and on the side
Multiply the first term in the top and first term in the left side for box #1
Multiply the second term in the top and first term in the left side for box #2
Multiply the first term in the top and second term in the left side for box #3
Multiply the second term in the top and second term in the left side for box #4
Simplify the expression by combining like terms
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9.2 - Multiplying Polynomials

14. 9.2 - Multiplying Polynomials
Assignment
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9.2 - Multiplying Polynomials

15. 9.2 - Multiplying Polynomials
Example 6
Multiply (x + 2)(x + 3)
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9.2 - Multiplying Polynomials

16. 9.2 - Multiplying Polynomials
Example 6 (using Box)
Multiply (x + 2)(x + 3)
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9.2 - Multiplying Polynomials

17. Example 6 Calculator Check
Multiply (x + 2)(x + 3)
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9.2 - Multiplying Polynomials

18. 9.2 - Multiplying Polynomials
Example 7
Multiply (x + 3)(x – 5)
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9.2 - Multiplying Polynomials

19. 9.2 - Multiplying Polynomials
Your Turn
Multiply (x – 3)(x – 5)
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9.2 - Multiplying Polynomials

20. 9.2 - Multiplying Polynomials
Example 8
Multiply (x – 5)(3x + 4)
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9.2 - Multiplying Polynomials

21. 9.2 - Multiplying Polynomials
Example 9
Multiply (x – 4)(3x + 2)
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9.2 - Multiplying Polynomials

22. 9.2 - Multiplying Polynomials
Your Turn
Multiply (4x – 1)(x + 5)
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9.2 - Multiplying Polynomials

23. 9.2 - Multiplying Polynomials
Example 10
Multiply (2x – 1)(5x + 3)
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9.2 - Multiplying Polynomials

24. 9.2 - Multiplying Polynomials
Example 11
Multiply (3x – 1)(4x + 9)
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9.2 - Multiplying Polynomials

25. 9.2 - Multiplying Polynomials
Your Turn
Multiply (8x + 11)(6x – 1)
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9.2 - Multiplying Polynomials

26. 9.2 - Multiplying Polynomials
Review
Add (x – 3) + (–x2 + 2x + 4)
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9.2 - Multiplying Polynomials

27. 9.2 - Multiplying Polynomials
Example 12
Multiply (x – 3)(–x2 + 2x + 4)
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9.2 - Multiplying Polynomials

28. 9.2 - Multiplying Polynomials
Example 13
Multiply (x + 2)(3x2 – 4x + 1)
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9.2 - Multiplying Polynomials

29. 9.2 - Multiplying Polynomials
Your Turn
Multiply (2x2 – 3x – 4)(x + 7)
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9.2 - Multiplying Polynomials

30. 9.2 - Multiplying Polynomials
Example 14
Find the perimeter and area of a rectangle which length is x – 5 and width is 3x + 1.
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9.2 - Multiplying Polynomials

31. 9.2 - Multiplying Polynomials
Example 15
Find the perimeter and area of a triangle which sides are x + 5 and height is x + 6.
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9.2 - Multiplying Polynomials

32. 9.2 - Multiplying Polynomials
Your Turn
Find the perimeter and area of a rectangle which length is x + 5 and width is 3x + 1.
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9.2 - Multiplying Polynomials

33. 9.2 - Multiplying Polynomials
Assignment
Worksheet
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9.2 - Multiplying Polynomials