1. Pre-Calculus Section 8.5a Binomial Expansion

3. Calculator Help Graphing calculator has n C r button. Math - PRB - nCr You must enter the n# before

5. Remember? (x + y) 0 (x + y) 1 (x + y) 2 (x + y) 3

6. Binomial Theorem Expands a binomial to any power (x + y) n = x n + nx n-1 y + …. + n C r x n-r y r +….nxy n-1 + y n * there are n + 1 terms * the power of the first term = n * the power of the last term = n

7. * the power of the rest of the terms decreases by 1 from left to right * the power of the rest of the terms decreases by 1 from right to left * the exponents add to equal n * find the coefficients using n C r * if subtracting alternate the signs

8. Write the expansion of (x + 2) 3 Binomial Expansion Coefficients: n = exponent the first term has a power of 3 3 C 0 = 1 st coefficient 3 C 1 = 2 nd coefficient 3 C 2 = 3 rd coefficient 3 C 3 = 4 th coefficient

9. 5.Write the expansion of (x + 2) 3

11. 6.Write the expansion of (y - 7) 4

13. 7.Write the expansion of (x + y) 5

15. 8.Write the expansion of (3x + 2y) 6

17. Homework: Page 624 2 – 10Evens 18 – 26Evens