Multiplying Polynomials “Two Special Cases”. Special Products: Square of a binomial (a+b) 2 = a 2 +ab+ab+b 2 = a 2 +2ab+b 2 (a-b) 2 =a 2 -ab-ab+b 2 =a.

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Presentation transcript:

Multiplying Polynomials “Two Special Cases”

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

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

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

MODEL: (a+b)(a+b) a2a2 ab b2b2

PRACTICE: (x+2) (x-2) (b+6) 2 (y-4) 2 x b b + 36 y 2 - 8y + 16