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GRADE 7 MATH LEARNING GUIDE Lesson 25, Exercises of Algebra

De La Salle Araneta University (DLSAU)Algebra

Grade 7 Math LESSON 25: SPECIAL PRODUCTS. LEARNING GUIDE ... Exercises. Find the product using the FOIL method. Write your answers on the spaces provided:.

Typology: Exercises

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Grade 7 Math LESSON 25: SPECIAL PRODUCTS LEARNING GUIDE
AUTHOR: Rechilda Villame
1!
GRADE 7 MATH LEARNING GUIDE
Lesson 25: Special Products Time: 3.5 hours
Prerequisite Concepts: Multiplication and Division of Polynomials
About the Lesson: This is a very important lesson. The applications come much later but the
skills will always be useful from here on.
Objectives:
In this lesson, you are expected to:
find (a) inductively, using models and (b) algebraically the
1. product of two binomials
2. product of a sum and difference of two terms
3. square of a binomial
4. cube of a binomial
5. product of a binomial and a trinomial
Lesson Proper:
A. Product of two binomials
I. Activity
Prepare three sets of algebra tiles by cutting them out from a page of newspaper or art
paper. If you are using newspaper, color the tiles from the first set black, the second set red and
the third set yellow.
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Partial preview of the text

Download GRADE 7 MATH LEARNING GUIDE Lesson 25 and more Exercises Algebra in PDF only on Docsity!

GRADE 7 MATH LEARNING GUIDE

Lesson 25 : Special Products Time: 3.5 hours Prerequisite Concepts : Multiplication and Division of Polynomials About the Lesson : This is a very important lesson. The applications come much later but the skills will always be useful from here on. Objectives: In this lesson, you are expected to: find (a) inductively, using models and (b) algebraically the

  1. product of two binomials
  2. product of a sum and difference of two terms
  3. square of a binomial
  4. cube of a binomial
  5. product of a binomial and a trinomial Lesson Proper : A. Product of two binomials I. Activity Prepare three sets of algebra tiles by cutting them out from a page of newspaper or art paper. If you are using newspaper, color the tiles from the first set black, the second set red and the third set yellow.

Problem:

  1. What is the area of a square whose sides are 2cm?
  2. What is the area of a rectangle with a length of 3cm and a width of 2cm?
  3. Demonstrate the area of the figures using algebra tiles. Problem:
  4. What are the areas of the different kinds of algebra tiles?
  5. Form a rectangle with a length of x + 2 and a width of x + 1 using the algebra tiles. What is the area of the rectangle? Solution:
  6. x 2 , x and 1 square units.

The area is the sum of all the areas of the algebra tiles. Area = x 2

  • x + x + x + 1 + 1 = x 2
  • 3 x + 2 Problem:
  1. Use algebra tiles to find the product of the following: a. b. c.
  2. How can you represent the difference x โ€“ 1 using algebra tiles? Problem:
  3. Use algebra tiles to find the product of the following: a. b. c. d.
  1. (4x + 3y) (2x + y)
  2. (7x โ€“ 8y) (3x + 5y) B. Product of a sum and difference of two terms I. Activity
  3. Use algebra tiles to find the product of the following: a. (x + 1) (x โ€“ 1) b. (x + 3) (x โ€“ 3) c. (2x โ€“ 1) (2x + 1) d. (2x โ€“ 3) (2x + 3)
  4. Use the FOIL method to find the products of the above numbers. II. Questions to Ponder
  5. What are the products?
  6. What is the common characteristic of the factors in the activity?
  7. Is there a pattern for the products for these kinds of factors? Give the rule. Concepts to Remember The factors in the activity are called the sum and difference of two terms. Each binomial factor is made up of two terms. One factor is the sum of the terms and the other factor being their difference. The general form is (a + b) (a โ€“ b). The product of the sum and difference of two terms is given by the general formula (a + b) (a โ€“ b) = a 2
  • b 2 . III. Exercises Find the product of each of the following:
  1. (x โ€“ 5) (x + 5)
  2. (x + 2) (x โ€“ 2)
  3. (3x โ€“ 1) (3x + 1)
  4. (2x + 3) (2x โ€“ 3)
  5. (x + y 2 ) (x โ€“ y 2 )
  6. (x 2
  • 10)(x 2
  1. (4xy + 3z 3 ) (4xy โ€“ 3z 3 )
  2. (3x^3 โ€“ 4)(3x^3 + 4)
  3. [(x + y) - 1] [(x + y) + 1]
  4. (2x + y โ€“ z) (2x + y + z) C. Square of a binomial I. Activity
  5. Using algebra tiles, find the product of the following: a. (x + 3) (x + 3) b. (x โ€“ 2) (x โ€“ 2)

c. (2x + 1) (2x + 1) d. (2x โ€“ 1) (2x โ€“ 1)

  1. Use the FOIL method to find their products. II. Questions to Ponder
  2. Find another method of expressing the product of the given binomials.
  3. What is the general formula for the square of a binomial?
  4. How many terms are there? Will this be the case for all squares of binomials? Why?
  5. What is the difference between the square of the sum of two terms from the square of the difference of the same two terms? Concepts to Remember The square of a binomial is the product of a binomial when multiplied to itself. The square of a binomial has a general formula,. III. Exercises Find the squares of the following binomials.
  6. (x + 5)^2
  7. (x - 5)^2
  8. (x + 4)^2
  9. (x โ€“ 4) 2
  10. (2x + 3) 2
  11. (3x - 2) 2
  12. (4 โ€“ 5x) 2
  13. (1 + 9x) 2
  14. (x^2 + 3y)^2
  15. (3x 3
  • 4y 2 ) 2 D. Cube of a binomial I. Activity A. The cube of the binomial (x + 1) can be expressed as (x + 1) 3 . This is equivalent to (x + 1)(x + 1)(x + 1).
  1. Show that (x + 1)^2 = x^2 + 2x + 1.
  2. How are you going to use the above expression to find (x + 1)^3?
  3. What is the expanded form of (x + 1) 3 ? B. Use the techniques outlined above, to find the following:
  4. (x + 2) 2
  5. (x โ€“ 1)^2
  6. (x โ€“ 2)^2 II. Questions to Ponder
  7. How many terms are there in each of the cubes of binomials?
  1. How many terms are in the product?
  2. What trinomial should be multiplied to to get?
  3. Is there a trinomial that can be multiplied to x โ€“ 1 to get x 3 + 1?
  4. Using the methods outlined in the previous problems, what should be multiplied to x + 2 to get x^3 + 8? Multiplied to x โ€“ 3 to get x^3 โ€“ 27? II. Questions to Ponder
  5. What factors should be multiplied to get the product x^3 + a^3? x^3 โ€“ a^3?
  6. What factors should be multiplied to get 27x 3
  • 8? Concepts to Remember The product of a trinomial and a binomial can be expressed as the sum or difference of two cubes if they are in the following form. III. Exercises A. Find the product.

B. What should be multiplied to the following to get a sum/difference of two cubes? Give the product.

Summary: You learned plenty of special products and techniques in solving problems that require special products.