1. Pg. 606 Homework
Pg. 606 #11 – 20, 34
#1 1, 8, 28, 56, 70, 56, 28, 8, 1
#2 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1
#3 a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5
#4 a6 – 6a5b + 15a4b2 – 20a3b3 + 15a2b4 – 6ab5 + b6
#5 x4 + 8x3y + 24x2y2 + 32xy3 + 16y4
#6 2187x7 – 5103x6y x5y2 – 2835x4y x3y4 – 189x2y5 + 21xy6 – y7
#8 a4 – 8a3b2 + 24a2b4 – 32ab6 + 16b8

2. 11.3 Binomial Theorem
Expand:
(3x– y4)3
(4x + y0.5)4

3. 11.3 Binomial Theorem Binomial Coefficients
Pascal’s Triangle works for relatively small values, but what if you want to expand something much larger?
We use a factorial to do so!
n! = 1 • 2 • 3 • … • n
3! =
8! =
If n and r are two nonnegative integers, the number called the binomial coefficient n choose r is defined by:

4. 11.3 Binomial Theorem
Binomial Theorem
Expand:
(x + y)5

5. 11.3 Binomial Theorem Binomial Theorem Examples:
Find the y12 term of: (x + y)15
Find the coefficient of the given term in the binomial expansion:
x3y4 term, (x + y)7
x8 term, (x + 5)11
x10 term, (x – 6)14

6. 11.3 Binomial Theorem Binomial Theorem Examples: Given: (2x – 1)10
Find the coefficient of the given term in the binomial expansion: x3 x8 x5