Download Homework for 9-2 - Stillman Valley High School

Homework for 9-3
p. 572 4, 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
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 !!!!
Use Square of a Binomial
Pattern
(a + b)2 = a2 + 2ab + b2
1. (2x + 5)2
“a” = 2x and “b” = 5
(2x)2 + 2(2x)(5) + (5)2
4x2 + 20x + 25
(a – b)2 = a2 - 2ab + b2
2. (3x – y) 2
“a” = 3x and “b” = y
(3x)2 - 2(3x)(y) + (y)2
9x2 - 6xy + y2
Sum & Difference Pattern
• Multiply: (x + 3)(x – 3)
o What happens to the middle term?
• (a + b)(a – b) = a2 – b2
• (r + 4)(r – 4)
o r2 - 16
• (5x + y)(5x – y)
o 25x2 – y2
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.
E
e
E
EE
Erect
Ee
Erect
e
Ee
Erect
Ee
Droopy
What percent of the possible gene
combinations of the offspring have droopy
ears?
EE
Ee
Erect
Erect
25%
Ee
Erect
Ee
Droopy
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