Algebra – Ch. 9.2Multiplying Polynomials

Mr. Deyo

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.

Learning Target

Home Work 1‐2‐3:  1) Class 4‐Square Notes Put In Binder?

2) Section 9.2TxtBk. Pg 531Problems 7, 13, 15, 17

29, 35, 41, 43Solved and Put in Binder?

Table of ContentsDate Description Date Due

3) Section _____Notes Copied on a

blank sheet of paper in Binder?

Storm Check (Think, Write, Discuss, Report)Questions on which to ponder and answer:1.How are the two images similar?2.How are they different?3.How can these two images be related to math?

1) FOIL (First, Outer + Inner, Last)

2) Polynomial

3) Binomial

4) Trinomial

Vocabulary

DAY 3 and/or DAY 41. Review the word

♦Friendly Definition♦Physical Representation

2. Show how the word works♦Synonyms/antonym♦Word Problems♦Related words/phrases♦Example/non-example

Friendly DefinitionFriendly DefinitionSketchSketch

WordworkWordwork SentenceSentence

DAY 21. Review word

♦Friendly Definition♦Physical Representation

2. Draw a sketch

DAY 51. Review the word

♦Friendly definition♦Physical Representation

3. Write a sentenceat least 2 rich words (1 action)correct spellingcorrect punctuationcorrect subject/predicate agreementclear and clean writing

DAY 11. Use Visuals

2. Introduce the word♦Friendly Definition♦Physical Representation

3. Use Cognates

4. Write friendly definition

5. Physical Representation

Word List1.2.3.4.

Word List1.2.3.4.

For use with pages xxx–xxxDaily Warm-Up Exercises For use with pages 527–533

Simplify –2 (9a –b)1.

2. Simplify r2s • rs3

3) Find the product 3x ( )2x3–

For use with pages xxx–xxxDaily Warm-Up Exercises For use with pages 527–533

Simplify –2 (9a –b)1.

2. Simplify r2s • rs3

ANSWER 18a 2b+–

ANSWER r3s4

3) Find the product 3x .( )2x3–

3x ( )2x3– = 3 • ( )2– • x • x3 Regroup factors.

Simplify.= –6x4

Notes: 3 Methods of Multiplying Polynomials:

*1) # by # Table 2) FOIL

(x + 2) (x + 2)

x2 + 4x + 4

(a + b) (c + d)

ac + ad + bc + bd

3) VerticalMultiplication

* Preferred Method

Multiply polynomials using a table Problem “A”

Find the product .( )x – 4 ( )3x + 2

Example 3

Multiply polynomials using a table Problem “A”

Find the product .

Example 3

( )x – 4 ( )3x + 2

SOLUTIONSTEP 1 Write subtraction as addition:

( )x – 4 ( )3x + 2 = x[ ]+ ( )4– ( )3x + 2

STEP 2 Make a table of products.

3x3x2x

4–

2 3x3x2x

4–

22x

12x– 8–

ANSWER3x2 2x+ – 12x 3x2 10x– – 8.– 8, orThe product is

Guided Practice Problems “B”

Find the product.

1. ( )3x5x3

2. ( )7x2x + 4

( )4n – 1 ( )n + 53.

ANSWER 15x4

Guided Practice Problems “B”

Find the product.

1. ( )3x5x3

2. ( )7x2x + 4 ANSWER 7x3 + 4x

( )4n – 1 ( )n + 53. ANSWER 4n2 + 19n – 5

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

_______________________________________.

Learning TargetBy 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.

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 ContentsDate Description Date Due

Multiply polynomials vertically or by using a table(Problem A)

Example 4

( )b2 + 6b – 7 ( ).3b – 4Find the productFind the productFind the product

+b2

+6b

-7

+3b -4

Multiply polynomials vertically or by using a table(Problem A Check)

Example 4

( )b2 + 6b – 7 ( ).3b – 4Find the productFind the productFind the product

3b3 ‐4b2

+18b2 ‐24b

‐21b +28 – 45b14b2+3b3 + 28

+b2

+6b

-7

+3b -4

Multiply polynomials verticallyExample 4

Find the product ( )b2 + 6b – 7 ( ).3b – 4Find the productFind the product

STEP 1 Multiply by 4.

SOLUTION–

b2 + 6b – 7

3b – 4×

– 24b + 284b2–

STEP 2 Multiply by 3b.

b2 + 6b – 7

3b – 4×

– 24b + 284b2–

– 21b18b2+3b3

Multiply polynomials verticallyExample 4

STEP 3 Add products.

b2 + 6b – 7

3b – 4×

– 24b + 284b2–

– 21b18b2+3b3

– 45b14b2+3b3 + 28

Multiply polynomials Problem BExample 5

( )2x2 + 5x – 1 ( ).4x – 3

+2x2

+6x

-1

+4x -3

Find the product

Multiply polynomials Problem BExample 5

( )2x2 + 5x – 1 ( ).4x – 3

+2x2

+6x

-1

+4x -3

+8x3 ‐6x2

+24x2 ‐18x

‐4x +3

Find the product

= 8x3 + 14x2 – 19x + 3

Multiply binomials using the FOIL patternExample 6

Find the product ( ).a – 2( )3a + 4

( )a – 2( )3a + 4

Write products of terms.

= 3a ( )a + + ( ) +( ) 3a ( )2( ) – 4( ) a ( )2–4( )

Multiply.= 3a2 + + 4a( )6a– + ( )8–

Combine like terms.

= 3a2 – 2a 8–

Guided Practice for Examples 4, 5, and 6

Find the product.

4. ( )x2 + 2x + 1 ( )x + 2

5. ( )3y2 – y + 5 ( )2y – 3

6. ( )4b – 5 ( )b – 2

ANSWER x3 + 4x2 + 5x + 2

ANSWER 6y3 – 11y2 + 13y – 15

ANSWER 4b2 – 13b + 10

Guided Practice for Examples 4, 5, and 6

Find the product.4. ( )x2 + 2x + 1 ( )x + 2

5. ( )3y2 – y + 5 ( )2y – 3

6. ( )4b – 5 ( )b – 2

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 ________________________________

_______________________________________.

Learning TargetBy 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.

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 ContentsDate Description Date Due

Vocabulary Review1) FOIL (First, Outer + Inner, Last)

2) Polynomial

3) Binomial

4) Trinomial

Example 7

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.

SKATEBOARDING

Solve a multi-step problem

Write a polynomial that represents the area of the skateboard park.

Example 7 Solve a multi-step problem

a. 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 – x33 – x

Example 7 Solve a multi-step problem

Area width= length • Formula for area of a rectangle

= ( )45 – x ( )33 – x 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