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Mastering Special Cases in Polynomial Multiplication

Learn how to multiply polynomials with two special cases: Square of a binomial and product of the sum and difference of two terms. Discover the patterns and rules to simplify calculations mentally. Practice with examples provided for better understanding.

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Mastering Special Cases in Polynomial Multiplication

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  1. 10.3 Multiplying Polynomials “Two Special Cases”

  2. Special Products: Square of a binomial = a2+ab+ab+b2 = a2+2ab+b2 (a+b)2 =a2-ab-ab+b2 =a2-2ab+b2 (a-b)2

  3. RULE: You can do this mentally when you recognize the pattern! (x+2)2 (x-6)2 x2 + 2x + 2x + 4 x2-12x+36 x2+4x+4

  4. Product of the sum and difference of two terms: (a+b) (a-b)=a2+ab-ab-b2 =a2-b2 The middle terms cancel out and you end up with the difference of perfect squares. (5x+2) (5x-2)= 25x2-4

  5. MODEL: (a+b)(a+b) a + b a2 ab a+b ab b2

  6. PRACTICE: (x+2) (x-2) x2 - 4 (b+6)2 b2 + 12b + 36 (y-4)2 y2 - 8y + 16

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