1. Algebra – Ch. 9.2 Multiplying Polynomials
Mr. Deyo

2. Learning Target
By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication.
I will demonstrate this by completing Four(4)-Square notes and by solving problems in a pair/group activity.

3. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 9.2
TxtBk. Pg 531
Problems 7, 13, 15, , 35, 41, 43
Solved and Put in Binder?
3) Section _____
Notes Copied on a blank sheet of paper in Binder?
Table of Contents
Date Description Date Due

4. Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer:
How are the two images similar?
How are they different?
How can these two images be related to math?
IMAGE 1
IMAGE 2

5. Vocabulary FOIL (First, Outer + Inner, Last) Polynomial Binomial
Trinomial

6. Vocabulary Acquisition
Friendly Definition
Sketch
Wordwork
Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 1
Use Visuals
Introduce the word
Friendly Definition
Physical Representation
Use Cognates
Write friendly definition
Word List
Vocabulary Acquisition
DAY 3 and/or DAY 4
1. Review the word
Friendly Definition
Physical Representation
2. Show how the word works
Synonyms/antonym
Word Problems
Related words/phrases
Example/non-example
DAY 5
1. Review the word
Friendly definition
Physical Representation
3. Write a sentence
at least 2 rich words (1 action)
correct spelling
correct punctuation
correct subject/predicate agreement
clear and clean writing

7. Daily Warm-Up Exercises
For use with pages xxx–xxx
For use with pages 527–533 1.
Simplify –2 (9a –b) 2.
Simplify r2s • rs3
3) Find the product 3x ( )
2x3 –

8. Daily Warm-Up Exercises
For use with pages xxx–xxx
For use with pages 527–533 1.
Simplify –2 (9a –b)
ANSWER
18a 2b + –
r3s4 2.
Simplify r2s • rs3
3) Find the product 3x ( )
2x3 – 3x ( )
2x3 – = 3 • ( ) 2 – x x3
Regroup factors.
Simplify. = –
6x4

9. 3 Methods of Multiplying Polynomials:
Notes:
3 Methods of Multiplying Polynomials:
*1) # by # Table
2) FOIL
3) Vertical Multiplication
(a + b) (c + d)
(x + 2) (x + 2)
x2 + 4x + 4
ac + ad + bc + bd
* Preferred Method

10. Example 3 Find the product . ( ) x – 4 3x + 2
Multiply polynomials using a table Problem “A”
Find the product ( ) x – 4 3x + 2

11. [ ] Example 3 Find the product . ( ) x – 4 3x + 2 SOLUTION
Multiply polynomials using a table Problem “A”
Find the product ( ) x – 4 3x + 2
SOLUTION
STEP 1 Write subtraction as addition: ( ) x – 4 3x + 2 = [ ]
STEP 2 Make a table of products. 3x
3x2 x 4 – 2 2x
12x 8
ANSWER
The product is
3x2 + 2x –
12x –
8, or
3x2
10x – 8.

12. Guided Practice Find the product. 1. ( ) 3x 5x3 2. ( ) 7x2 x + 4 ( )
Problems “B”
Find the product. 1. ( ) 3x
5x3 2. ( )
7x2 x + 4 ( ) 4n – 1 n + 5 3.

13. Guided Practice Find the product. 1. ( ) 3x 5x3 ANSWER 15x4 2. ( ) 7x2
Problems “B”
Find the product. 1. ( ) 3x
5x3
ANSWER
15x4 2. ( )
7x2 x + 4
ANSWER
7x3 + 4x ( ) 4n – 1 n + 5 3.
ANSWER
4n2 +
19n – 5

14. Storm Check (Think, Write, Discuss, Report)
If multiplying polynomials, how would you modify the table for a binomial by a trinomial (2 x 3) or a trinomial by a trinomial (3 x 3)? For a binomial multiplied by a trinomial (2 x 3), I _______________________________________. For a trinomial multiplied by a trinomial (3 x 3), I

15. Learning Target
By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication.
I will demonstrate this by completing Four(4)-Square notes and by solving problems in a pair/group activity.

16. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section ______ 3) Section ______
TxtBk. Problems_________ Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

17. -4 +3b +b2 +6b -7 Example 4 Find the product Find the product
Multiply polynomials vertically or by using a table (Problem A)
Find the product
Find the product
Find the product ( ) b2 + 6b – 7 ). 3b 4
+3b -4
+b2
+6b -7

18. 3b3 -4b2 +18b2 -24b -21b +28 +3b -4 +b2 +6b -7 – 45b 14b2 + 3b3 28
Example 4
Multiply polynomials vertically or by using a table (Problem A Check)
Find the product
Find the product
Find the product ( ) b2 + 6b – 7 ). 3b 4
+3b -4
3b3
-4b2
+18b2
-24b
-21b
+28
+b2
+6b -7 –
45b
14b2 +
3b3 28

19. Example 4 Find the product Find the product Find the product ( ) b2 +
Multiply polynomials vertically
Find the product
Find the product
Find the product ( ) b2 + 6b – 7 ). 3b 4
STEP 1 Multiply by 4.
SOLUTION – b2 + 6b 7 3b 4 
STEP 2 Multiply by 3b. b2 + 6b – 7 3b 4  –
24b + 28
4b2 –
24b + 28
4b2 –
21b
18b2 +
3b3

20. Example 4 STEP 3 Add products. b2 + 6b – 7 3b 4  – 24b + 28 4b2 – 21b
Multiply polynomials vertically
STEP 3 Add products. b2 + 6b – 7 3b 4  –
24b + 28
4b2 –
21b
18b2 +
3b3 –
45b
14b2 +
3b3 28

21. -3 +4x +2x2 +6x -1 Example 5 Find the product ( ) 2x2 + 5x – 1 ( ). 4x
Multiply polynomials Problem B
Find the product ( )
2x2 + 5x – 1 ( ). 4x – 3
+4x -3
+2x2
+6x -1

22. +8x3 -6x2 +24x2 -18x -4x +3 -3 +4x +2x2 +6x -1 Example 5
Multiply polynomials Problem B
Find the product ( )
2x2 + 5x – 1 ( ). 4x – 3
+4x -3
+8x3
-6x2
+24x2
-18x
-4x +3
+2x2
+6x -1 =
8x3 +
14x2 –
19x 3

23. Example 6 Find the product ( ) 3a + 4 ( ). a – 2 ( ) a – 2 3a + 4 = 3a
Multiply binomials using the FOIL pattern
Find the product ( ) 3a + 4 ( ). a – 2 ( ) a – 2 3a + 4
Write products of terms. = 3a ( ) a + 2 – 4
Multiply. =
3a2 + 4a ( ) 6a – 8
Combine like terms. =
3a2 – 2a 8

24. Guided Practice Find the product. 4. ( ) x2 + 2x 1 x 2 ANSWER x3 + 4x2
for Examples 4, 5, and 6
Find the product. 4. ( ) x2 + 2x 1 x 2
ANSWER x3 +
4x2 5x 2 5. ( )
3y2 – y + 5 2y 3
ANSWER
6y3 –
11y2 +
13y 15 6. ( ) 4b – 5 b 2
ANSWER
4b2 –
13b + 10

25. Guided Practice Find the product. 4. ( ) x2 + 2x 1 x 2 6. ( ) 4b – 5 b
for Examples 4, 5, and 6
Find the product. 4. ( ) x2 + 2x 1 x 2 6. ( ) 4b – 5 b 2 5. ( )
3y2 – y + 5 2y 3

26. Storm Check (Think, Write, Discuss, Report)
Of the three methods to multiply polynomials, which do you prefer to use? Why? I prefer to use the ______________ method because ________________________________ _______________________________________.

27. Learning Target
By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication.
I will demonstrate this by completing Four(4)-Square notes and by solving problems in a pair/group activity.

28. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section ______ 3) Section ______
TxtBk. Problems_________ Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

29. Vocabulary Review FOIL (First, Outer + Inner, Last) Polynomial
Binomial
Trinomial

30. Write a polynomial that represents the area of the skateboard park.
Example 7
Solve a multi-step problem
SKATEBOARDING
You are designing a rectangular skateboard park on a lot that is on the corner of a city block. The park will be bordered by a walkway along two sides. The dimensions of the lot and the walkway are shown in the diagram.
Write a polynomial that represents the area of the skateboard park. 30

31. Write a polynomial using the formula for the area of
Example 7
Solve a multi-step problem
Write a polynomial using the formula for the area of
a rectangle. The park’s length is the lot’s length minus the width of the sidewalk, or Similarly,
the park’s width is
SOLUTION 45 – x 33 31

32. (45-3) (33-3) (42)(30) 1260 square feet Example 7 Area width = length
Solve a multi-step problem
Area
width =
length •
Formula for area of a
rectangle = ( ) 45 – x 33
Substitute for length
and width. =
1485 –
45x
33x + x2
Multiply binomials. =
1485 –
78x + x2
Combine like terms.
b. What is the area of the park if the walkway is 3 feet wide?
(45-3) (33-3)
(42)(30)
1260 square feet 32