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.
Mastering Special Cases in Polynomial Multiplication
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Presentation Transcript
10.3 Multiplying Polynomials “Two Special Cases”
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
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
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
MODEL: (a+b)(a+b) a + b a2 ab a+b ab b2
PRACTICE: (x+2) (x-2) x2 - 4 (b+6)2 b2 + 12b + 36 (y-4)2 y2 - 8y + 16
