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Exploring Special Products of Binomials: Strategies and Applications

In this lesson, students will learn to read, write, and classify polynomials, while focusing on finding special products of binomials. Key concepts include perfect square trinomials and the difference of two squares. Through various examples, students will explore how to multiply binomials in different forms, such as (a + b)², (a - b)², and (a + b)(a - b). The lesson also emphasizes word problems involving binomials, enhancing students' understanding of practical applications in geometry and algebra.

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Exploring Special Products of Binomials: Strategies and Applications

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  1. Algebra 1 7.8 Special Products of Binomials

  2. Learning Targets Language Goal • Students should be able to read, write, say, and classify polynomials. Math Goal • Students should be able to find special products of binomials. Essential Question • What are the characteristics that make binomials so special?

  3. Warm-up

  4. Vocabulary Perfect Square Trinomial: A trinomial whose factored form is the square of a binomial. A perfect-square trinomial has the form: or Difference of two squares: A polynomial of the form which can be written as the product

  5. Example Type 1: Finding Products in the Form (a + b)² Multiply A. (a + 4)² B. (3x + 2y)²

  6. Example Type 1: Finding Products in the Form (a + b)² Multiply C. D. ²

  7. Example Type 2: Finding Products in the Form (a – b)² Multiply A. (x – 5)² B. (6a – 1)²

  8. Example Type 2: Finding Products in the Form (a – b)² Multiply C. (4c – 3d)² D. (3 – x²)²

  9. Example Type 3: Finding Products in the Form (a + b)(a – b) Multiply A. B.

  10. Example Type 3: Finding Products in the Form (a + b)(a – b) Multiply C.D.

  11. Example Type 4: Word Applications A. A square koi pond is surrounded by a gravel path. Write an expression that represents the area of the path.

  12. Example Type 4: Word Applications

  13. Lesson Quiz

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