1. The Binomial Theorem Unit 10.5

2. Binomial Theorem (a + b) 0 = 1a 0 b 0 (a + b) 1 = 1a 1 b 0 + 1a 0 b 1 (a + b) 2 = 1a 2 b 0 + 2a 1 b 1 + 1a 0 b 2 (a + b) 3 = 1a 3 b 0 + 3a 2 b 1 + 3a 1 b 2 + 1a 0 b 3 (a + b) 4 = 1a 4 b 0 + 4a 3 b 1 +6a 2 b 2 + 4a 1 b 3 + 1a 0 b 4 (a + b) 5 = 1a 5 b 0 + 5a 4 b 1 +10a 3 b 2 +10a 2 b 3 + 5a 1 b 4 + 1a 0 b 5 Complete the next 5 binomial expansions

3. Practical Implication 1.Computer programming 1 0 2.Physics: Comparing earths’ radius to its height or weight 3.Easier way to add numbers

4. Practice Problems Page 629 1b (2x + 3y) 5 Identify the polynomial that will be computed 1a 5 b 0 + 5a 4 b 1 +10a 3 b 2 +10a 2 b 3 + 5a 1 b 4 + 1a 0 b 5 32x 5 + 240x 4 y +720x 3 y 2 +1080x 2 y 3 + 810xy 4 + 243y 5

5. Practice Problems Page 629 Guided 2a page 629 (2x – 7) 3 Pascal 1a 3 b 0 + 3a 2 b 1 + 3a 1 b 2 + 1a 0 b 3 8x 3 - 84x 2 + 294x 3 – 343 Page 633 Problems 1 - 10

6. Find binomial coefficients Formula n C r = n! (n – r)!r! r = term in the coefficient r = k – 1 (x + y) 9, 6 th term n = 9 r = 5 n C r = 9! = 9! = 9*8*7*6*5*4*3*2*1 = 126 (9 – 5)!5! 4!5! 4*3*2*1*5*4*3*2*1

7. Binomials with coefficients other than 1 (2x – 3y) 8, x 3 y 5 n = 8 r = 5 a = 2x b = (-3y) n C r = n! 8! → 8*7*6 = 56 (n – r)!r! 3!5! 3*2*1 56(2x) 3 (-3y) 5 = 56(8)(-243) = -108,864

8. Exercises Page 633 Problems 11 - 18