# Algebra and Trigonometry - download pdf or read online By Harley Flanders and Justin J. Price (Auth.)

ISBN-10: 012259665X

ISBN-13: 9780122596650

Algebra and Trigonometry

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Extra resources for Algebra and Trigonometry

Sample text

X + y + z)(x + / - z) 21. (x2 + y2)(x2 - 3y2) 22. (x4 - y4)(x4 + y4) 23. (x + 7 + z)2 24. (ax + by + cz)(cx + Ζτμ + az) 25. (r + \)(s + 1)(/ + 1) 26. (r + *)(r - s)2 27. (a + Z>)(a + 2b)(a + 3Z>) 28. (a + &)(& + c)(c + a) 29. (x2 + 2xy - 2y2)(x2 - 2xy + 2y2) 30. (x + y + z)(x2 + 7 2 + z2 — xy — yz — zx). Is the expression a perfect square? If so, of what? 31. x2 + 16x + 64 32. y4 + 2y2 + 1 33. z 6 + 4z3 + 4 34. I602 + 80 + 1 35. x2y2 + 3x^ + 9 36. 9c2 - 30a/ + 25d2 37. (x2 + l) 2 + 2(x2 + 1) + 1 38.

JC1/2+73/2)2 23. u1/3(2u2/3 - u~1/6) 24. 19. (^4/3^-2/3)3 (*4^~8)5/2 ^ - 2 16· L» 1/3 (8L> 6 )- 2/3 . Express in terms of at most a single radical: 25. y/2-yï 26. VT^ 29. ( - A ) * 30. VbVb 27. {tf/γϊό 28. -^2L 31. V^-V^-V^ 3 32. V^-V^'V^· Express without radicals, using only positive exponents: 33. d/xj2)-3'5 34. -s/{xy2)-w3/(x2y)-wt 35. (\/jc 14 y- 21/5 )- 3 / 7 36. 4/5 JÖ · \ y ) \ z ) \ w ) \ χ ) ' 8. POLYNOMIALS In this section we study properties of the most common algebraic expressions, polynomials.

Verify the formulas: 39. Va 2 + * 2 = fl / l + ( - V 40. V * 2 + 1 - V3 - 3 Prove for w-th roots: 43. rule (1) 44. rule (2) 45. rule (3) VA:2 4- 1 46. rule (4). 7, y/5 ^ 2 . 2 to estimate 47. V6 48. VÏÔ 49. VV5 50. 51. V3Ö 52. V75 53. V4Ö 54. Prove: 55. V5 + 2V6 = \/2 + V3 57. V9 - 2 \ / Ï 4 = V7 - \/2 V*2 + 1 V2/3 y/ÏÏ6. 56. yfr - 2 \/6 = \/3 - y/l 58. \/δ + 2 >/Ϊ5 = λ/3 + V5. 7. RATIONAL EXPONENTS What meaning can we give to am/n, where m/n is a rational number not necessarily an integer?