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tive numbers, arranged in order of magnitude, of which a and b, are respectively the greatest, shew that

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than if the denominators b1, b2, ... b, were arranged in other

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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

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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.

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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.

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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*.

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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).

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3. (x-1)(x+2).

5. (x+1)2(x-1). 7. 16x1-1.

VII. 1. (2x2+3x-2) (3x+1). 2. (3x – 2) (4x3 – 4x3 — x + 1). 4. (x3-9x+23x-15)(x-7).

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equal to 5 (1+x2), and the denominator to (1 + x2); so that the

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