Special Products

Special Products Math A (Grade 9) Section 8-8 Special Products

Materials: chalkboard/whiteboard chalk/markers calculators worksheets algebra tiles (overhead-Only if you want to use it. I have algebra tiles for the overhead if you want to use them.) ***All worksheets and algebra tiles will be provided***

Lesson Overview: Students will learn how to find squares of sums and differences and find the product of a sum and a difference by using the distributive method, algebra tiles, and the area of a square to determine the rules based on their answers.

Lesson Objectives: Students will be able to compare the different methods of finding products of binomials. (Analysis) Students will be able to evaluate which method of finding the squares of sums and differences and products of a sum and a difference works best for them. (Evaluation)

NYS Standards:  Key Idea 3 – Operations o Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions (3A) . Multiplication of polynomials

Anticipatory Set: Time? Give the students the Special Products worksheet and have them complete the review problem using the distributive method. Have one student come to the board and model for the rest of the group how he solved it.

Developmental Activity: Time? 1. Have the students read Example 1 for Square of a Sum. Ask: What do you think the answer is? ( common mistake: x2 + 72 ) But what do you do when you square something? (you multiply the term by itself) Have you done that? Show the students how to write it out as a product of two binomials. Emphasize the importance of writing it out this way so they don’t make the common mistake of above. Have the students solve the problem using the distributive method. 2. Then model for the students how to complete Example 1 using algebra tiles. Go over the answer as a class, discussing how they used the algebra tiles. Discuss how this relates to using the distributive property. 3. Have students complete the first part of Example 2 on their own or with a partner using the distributive method. Go over the answer as a class. 4. Then model for the students how to complete Example 2 by computing the area of a square. Go over the answer, discussing how they used this method and how it is related to using algebra tiles and using the distributive method. 5. Have the students complete Example 3 on their own or with a partner using the distributive method. 6. Have the students complete the problem with their choice of either algebra tiles or computing the area of a square. Go over the answer as a class using all three methods. 7. If there is time, have the students complete the example problems at the end of the worksheet on their own or with a partner. If there is not time, they can finish the problems for homework.

Closure: Time? Discuss as a class what the students learned today. How does what we did today relate to what you learned yesterday? (It’s the same, only you are either multiplying the same two binomials together or binomials with a sum and difference.) Ask: Which method did you like best and why? Discuss how they can’t have algebra tiles on the Math A exam, but they can draw their own on the test paper.

Assessment: Time? Give the students the Exit Ticket and have them turn it in before they leave. Name: ______Period: ______

Special Products

Review: Solve the given problem using the distributive method. Show all work.

(x + 5)(2x - 3)

You can always use the distribution method to find the product of two binomials however, there are some pairs of binomials that follow a specific pattern.

Square of a Sum: (a + b)2 = (a + b)(a + b)= a 2 + 2ab + b 2

2 Example 1: (x + 3)

Rewrite:

Use the distributive property:

Use algebra tiles: Square of a Difference: (a - b)2 = (a - b)(a - b)= a 2 - 2ab + b 2

Example 2: (x - 4)2

Rewrite:

Use the area of a square: x + (-4)

Product of a Sum and a Difference: (a + b)(a - b)= a 2 - b 2

Example 3: (x + 9)(x - 9)

Use algebra tiles or the area of a square: Example Problems

Directions: Find each product using any method you choose. Show all work!!!

1. (x + 8)(x - 8)

2 2. (3x - 4)

2 3. (5x +1)

Challenge! 2 (x + 5y)

Name: ______Period: ______

Exit Ticket

Directions: Find the product using whatever method you choose. Show all work!

2 (2x + 5)

Name: ______Answer Key______Period: ______

Special Products

Review: Solve the given problem using the distributive method. Show all work.

(x + 5)(2x - 3) 2x 2 - 3x +10x - 15 2x 2 + 7x - 15

You can always use the distribution method to find the product of two binomials however, there are some pairs of binomials that follow a specific pattern.

Square of a Sum: (a + b)2 = (a + b)(a + b)= a 2 + 2ab + b 2

2 Example 1: (x + 3)

Rewrite: (x + 3)(x + 3)

2 x + 3x + 3x + 9 x 2 + 6x + 9

Use algebra tiles: Square of a Difference: (a - b)2 = (a - b)(a - b)= a 2 - 2ab + b 2

Example 2: (x - 4)2

Rewrite: (x - 4)(x - 4)

2 x - 4x - 4x +16 x 2 - 8x +16

Use the area of a square: x + (-4)

x 2 x -4x +

(-4) -4x 16 x 2 + (- 4x) + (- 4x) +16

x 2 - 8x +16

Product of a Sum and a Difference: (a + b)(a - b)= a 2 - b 2

Example 3: (x + 9)(x - 9)

x 2 + 9x - 9x - 81 x 2 - 81

Use algebra tiles or the area of a square: Example Problems

Directions: Find each product using any method you choose. Show all work!!!

1. (x + 8)(x - 8)

x 2 - 16x +16x - 64 2 x - 64

2 2. (3x - 4)

(3x - 4)(3x - 4) 2 9x - 12x - 12x +16 9x 2 - 24x +16

2 3. (5x +1)

(5x +1)(5x +1) 2 25x + 5x + 5x +1 25x 2 +10x +1

Challenge! 2 (x + 5y)

(x + 5y)(x + 5y) 2 2 x + 5xy + 5xy + 25y x 2 +10xy + 25y 2

Name: ______Answer Key______Period: ______

Exit Ticket

Directions: Find the product using whatever method you choose. Show all work!

2 (2x + 5)

(2x + 5)(2x + 5) 2 4x +10x +10x + 25 4x 2 + 20x + 25