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Homework for 9-3

Learn how to use special product patterns to multiply polynomials, including the square of a binomial and the sum and difference patterns. Also, discover how polynomials can be used to model gene combinations in dogs.

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Homework for 9-3

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  1. Homework for 9-3 p. 572 4, 5, 8, 10, 12, 15, 16, 20, 24, 28, 30, 33, 36, 40, 43, 50, 53

  2. 9-3 Special Products of Polynomials Objective: use special product patterns to multiply polynomials

  3. Square of a Binomial • (a + b)2 = a2 + 2ab + b2 • Because (a + b)2 means (a + b)(a + b) • (a – b)2 = a2 - 2ab + b2 • Because (a – b) means (a – b)(a – b) • NOTE: Don’t make this mistake! • (a + b)2 a2 + b2 and (a – b)2  a2 – b2 !!!!

  4. Use Square of a Binomial Pattern (a + b)2 = a2 + 2ab + b2 • (2x + 5)2 “a” = 2x and “b” = 5 (2x)2 + 2(2x)(5) + (5)2 4x2 + 20x + 25 (a – b)2 = a2 - 2ab + b2 • (3x – y) 2 “a” = 3x and “b” = y (3x)2 - 2(3x)(y) + (y)2 9x2 - 6xy + y2

  5. Sum & Difference Pattern • Multiply: (x + 3)(x – 3) • What happens to the middle term? • (a + b)(a – b) = a2 – b2 • (r + 4)(r – 4) • r2 - 16 • (5x + y)(5x – y) • 25x2 – y2

  6. Mental Math • 20 x 20 = 400 easy….. • 18 x 22 = ? Not so easy….. • But think of it this way: 18 is 2 less than 20 and 22 is 2 more than 20 so that… • 18 x 22 = (20 - 2) x (20 + 2) = 400 – 4 = 396

  7. Canine Genetics • In dogs, the gene E is for erect ears and the gene e is for droopy ears. Any gene combination with an E results in erect ears. The Punnett square shows the possible gene combinations of the offspring and the resulting type of ear. E e E e

  8. What percent of the possible gene combinations of the offspring have droopy ears? 25% Show how you could use a polynomial to model the possible gene combinations of the offspring. One dog = (.5E + .5e) Two dogs with same genes = (.5E + .5e)2 Expanded: .25E2 + .5Ee + .25e2

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