1079 11.4 The Binomial Theorem CONCEPT PREVIEWFill in the blank(s) to correctly complete each sentence. 1. Each number that is not a 1 in Pascal’s triangle is the of the two numbers directly above it (one to the right and one to the left). 2. The value of 8! is . 3. The value of 0! is . 4. The value of 7C3 is . 5. 12C4 = 12C (Do not use 4 in the blank.) 6. In the expansion of 1x + y25, the number of terms is . 7. In the expansion of 1x + y28, the first term is and the last term is . 8. The sum of the exponents on x and y in any term of the expansion of 1x + y210 is . 9. The second term in the expansion of 1p + q25 is . 10. The fourth term in the expansion of 12x - y27 is . 11.4 Exercises Evaluate each binomial coefficient. In Exercises 21 and 22, leave answers in terms of n. See Example 1. 11. 6! 3!3! 12. 5! 2!3! 13. 7! 3!4! 14. 8! 5!3! 15. a 8 5b 16. a 7 3b 17. a 10 2 b 18. a 9 3b 19. a 14 14b 20. a 15 15b 21. a n n - 1b 22. a n n - 2b 23. 8C3 24. 9C7 25. 100C98 26. 20C5 27. 9C0 28. 4C0 29. 12C1 30. 5C1 Write the binomial expansion of each expression. See Examples 2–4. 31. 1x + y26 32. 1m+ n24 33. 1p - q25 34. 1a - b27 35. 1r2 + s25 36. 1m+ n224 37. 1p + 2q24 38. 13r + s26 39. 17p - 2q24 40. 14a - 5b25 41. 13x - 2y26 42. 17k - 9j24 43. a m 2 - 1b 6 44. a3 - y 3b 5 45. a22r + 1 mb 4 46. a 1 k + 23pb 3 47. a 1 x4 + x4b 4 48. a 1 y5 + y5b 5
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