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

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

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

Use Square of a Binomial Pattern (a + b) 2 = a 2 + 2ab + b 2 1.(2x + 5) 2 “a” = 2x and “b” = 5 (2x) 2 + 2(2x)(5) + (5) 2 4x x + 25 (a – b) 2 = a 2 - 2ab + b 2 2.(3x – y) 2 “a” = 3x and “b” = y (3x) 2 - 2(3x)(y) + (y) 2 9x 2 - 6xy + y 2

Sum & Difference Pattern Multiply: (x + 3)(x – 3) o What happens to the middle term? (a + b)(a – b) = a 2 – b 2 (r + 4)(r – 4) o r (5x + y)(5x – y) o 25x 2 – y 2

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

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. EE Erect Ee Erect Ee Erect Ee Droopy Ee EeEe

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:.25E 2 +.5Ee +.25e 2 EE Erect Ee Erect Ee Erect Ee Droopy