Algebra – Ch. 9.2 Multiplying Polynomials Mr. Deyo

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.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 9.2 TxtBk. Pg 531 Problems 7, 13, 15, 17 29, 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

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

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

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

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 –

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

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

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

[ ] 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.

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.

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

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 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.

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

-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

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

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

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

-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

+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

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

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

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

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 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.

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

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

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

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

(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