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Mastering Polynomial Multiplication: Techniques and Examples for Success

Dive into the essential techniques for multiplying polynomials, including monomials and binomials. This guide presents a variety of examples demonstrating how to apply the Distributive Property effectively. Explore challenging cases like multiplying polynomials with multiple terms and discover how to formulate expressions for real-world geometric problems. You'll find step-by-step solutions and practical quizzes to reinforce your understanding. Sharpen your algebra skills and boost your confidence in polynomial multiplication!

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Mastering Polynomial Multiplication: Techniques and Examples for Success

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  1. 9. Multiply.

  2. 10. Multiply. (3x3)(6x2)

  3. Example 2A: Multiplying a Polynomial by a Monomial Multiply. 4(3x2 + 4x – 8)

  4. Example 2B: Multiplying a Polynomial by a Monomial Multiply. 6pq(2p – q)

  5. Example 2C: Multiplying a Polynomial by a Monomial Multiply. 1 ( ) 2 2 2 x y 6 + xy 8 x y 2

  6. Check It Out! Example 2 Multiply. a. 2(4x2 + x + 3)

  7. Check It Out! Example 2 Multiply. c. 5r2s2(r – 3s)

  8. To multiply a binomial by a binomial, you can apply the Distributive Property more than once: (x + 3)(x + 2) =

  9. Example 3A: Multiplying Binomials Multiply. (s + 4)(s – 2)

  10. Example 3B: Multiplying Binomials Multiply. (x –4)2

  11. Example 3C: Multiplying Binomials Multiply. (8m2 – n)(m2 – 3n)

  12. Check It Out! Example 3a Multiply. (a + 3)(a – 4)

  13. Check It Out! Example 3b Multiply. (x – 3)2

  14. Check It Out! Example 3c Multiply. (2a – b2)(a + 4b2)

  15. To multiply polynomials with more than two terms, you can use the Distributive Property several times. Multiply (5x + 3) by (2x2 + 10x – 6): (5x + 3)(2x2 + 10x– 6) =

  16. Example 4A: Multiplying Polynomials Multiply. (x – 5)(x2 + 4x – 6)

  17. Example 4B: Multiplying Polynomials Multiply. (2x – 5)(–4x2 – 10x + 3)

  18. Example 4C: Multiplying Polynomials Multiply. (x + 3)3

  19. Example 4D: Multiplying Polynomials Multiply. (3x + 1)(x3 + 4x2 – 7) –7 x3 4x2 3x +1

  20. Check It Out! Example 4a Multiply. (x + 3)(x2 – 4x + 6)

  21. Check It Out! Example 4b Multiply. (3x + 2)(x2 – 2x + 5)

  22. Check It Out! Example 5 The length of a rectangle is 4 meters shorter than its width. a. Write a polynomial that represents the area of the rectangle.

  23. Check It Out! Example 5 The length of a rectangle is 4 meters shorter than its width. b. Find the area of a rectangle when the width is 6 meters.

  24. Lesson Quiz: Part I Multiply. 1. (6s2t2)(3st) 2. 4xy2(x + y) 3. (x + 2)(x – 8) 4. (2x – 7)(x2 + 3x – 4) 5. 6mn(m2 + 10mn – 2) 6. (2x – 5y)(3x + y)

  25. Lesson Quiz: Part II 7. A triangle has a base that is 4cm longer than its height. a. Write a polynomial that represents the area of the triangle. b. Find the area when the height is 8 cm.

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