tive numbers, arranged in order of magnitude, of which a and b, are respectively the greatest, shew that than if the denominators b1, b2, ... b, were arranged in other n any a+b 24. If a be less than b, shew that the logarithm of (9) *** can be expanded in a series of which the general term is 3. a* - a2b2+2ab3 — b1. 5. a*+4a3x + 4α2x2 - x2. 7. ab+(a-b)x-2ax-x3. 9. 6x* -96. 2. 7a+16a2b— ab2 – 10b3. 4. a* - a3b2 + 4ab3 — 4b1. 6. a* - 8α2x2 + 16x*. 8. 60x+42x a-107x a2+10xα+14a*. 10. 4x3-22xy + 42xy - 27y. 11. 12x-17xy+3xy2+2y3. 12. x - x1y2+ x3y* — yo. 24. a*x*. 22. x-7x+ 21x3 — 17x1 — 25x3 + 6x2 - 2x-4. 23. a3 + 2a + 3a2 + 2a2 + 1. 25. x-10x2 + 9. 26. x + x + 1. - 27. x3-x3a2+2×3ab−(b2+2ac)x2+2x3 (bc+ad) − (c3+2bd) x2+2xcd—d3. 30. abc+(ab+bc + ca)x + (a + b + c) x3 + x3. 31. x − x3 (a+b+c+d) + x2 (ab+ac + ad + bc + bd + cd) -x(bcd+acd+abd+abc) + abcd. 33. b2 - d2. 32. 26°c2 + 2c3a2 + 2a3b3 — a* — ba — c*. 31. b+c-a. 34. a2 + ax + x3. 36. ab+bc + ca. 39. ab ac + b2 - c2. 42. (a+b-c-d) (a-b+c-d). 45. The quotient is 7xy (x+y). 46. Each is abc - ap2 - bq- cr2+2pqr. 47. (a−x) (a + x) (a2 + x2) (a* + x1) (a3 + x3). 48. (a+b+c) (b+c-a) (a−b+c) (a + b−c). 49. (b+c+d− a) (a + c + d − b) (a + b + d −c) (a + b + c − d). |