By Charles Denlinger and Elaine Jacobson (Auth.)
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Extra info for Algebra Review
The symbol for the coeffi cient of x ~kyk ± tfie expansion of (x + y ) is n n n n For example, Thus (2) - 1 . (J) - s . ( ) • io, ( ) - io, (>) - , , g ) - 1 . 5 2 5 3 There is a way to calculate the binomial coefficients direct ly, without using Pascal's triangle. We begin by defining m-factorial for any positive integer m: m! = 1*2*3 • m. Thus 1! = 1 2! = 1 - 2 = 2 3! = 1-2-3 = 6 4! = 1-2-3-4 = 24 5! = l*2-3-4-5 - 6 = 120 6! = 1-2-3-4-5 = 720 etc. For completeness, we define 0! = 1 . It can then be shown that for all integral values of n and k such that 0 £ k £ n, (1) For example, if we follow this formula, then (i) a) (remember, 0!
14. L5. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 50. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. i . [i - ( i . (i 51. 1 INTRODUCTION If 2 is substituted in the equation 3x- 2 = 4 the two sides become equal. We say that x = 2 is a solution of the equation. The following operations are helpful for finding the solu tions of an equation: I. II. The same quantity may be added to or subtracted from both sides of an equation. Both sides of an equation may be multiplied (or divided) by the same non-zero quantity.
2 7 4 , writing down the 41. 10. Find each of the following: (a) 11. 7! (b) 8! ) Use cancellation, as in 7*12 = 84 In problems 12-20, find only the term specified, using formula (3). 12. The fourth term in ( 2 x - y ) 13. The second term in ( 4 x + 3 y ) ^ 14. The third term in ( a b - 3 c ) 15. The middle term in ( x - 3 y ) 16. The next to last term in (a + 4 b ) 17. The fourth term in ( x - 2 y ) 7 2 2 8 6 2 5 1 2 4 7 18. The term involving x in (3x+4y) 19. The term involving x 6 in ( 2 x - l ) 20.
Algebra Review by Charles Denlinger and Elaine Jacobson (Auth.)