By J. Hamblin Smith
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23. (x+1)^ 24. (x-1)^ 26. (a2-62)^ 27. {n + b + cf. 28. (a-b-cy. 25. (x + 2)l 30. {rti + ny. {171^ — 11^). 29. {m - n)'. : 21. An 68. ssion of 5 dimensions. DIVISION. 69. An each of its Thus x^ 33 algebraical expression is called homogeneovs terms is + xy + y- of the is when same dimensions. homogeneous, for each term is of 2 dimen- sions. Also 3x^ + 4x-i/ + 5y^ is homogeneous, for each term is of 3 dimensions, the numerical coeiiicients not affecting the dimensions of each term. An 70. expression i-; said to he arranged according to when the indices of that letter occur in the order of their magnitudes, either increasing or decreasing.
15. x- + 2x-3. + y--z'^. 13. 2x2-7x4-9, 16. x*-4xh/ + y*. 18. ^. 19. x + 2y-Sz. x 14. 17. a^ + P + c^. 20. X- - 2)/2 5. 10. + y\ x^ x-y + z. + 52*, Expand the following expressions 22. (x-a)'. {x + (if. 23. (x+1)^ 24. (x-1)^ 26. (a2-62)^ 27. {n + b + cf. 28. (a-b-cy. 25. (x + 2)l 30. {rti + ny. {171^ — 11^). 29. {m - n)'. : 21. An 68. ssion of 5 dimensions. DIVISION. 69. An each of its Thus x^ 33 algebraical expression is called homogeneovs terms is + xy + y- of the is when same dimensions. homogeneous, for each term is of 2 dimen- sions.
57. 9x + Sx* + 14x^ + 2 by 1 + 5x + x^. 12j:S + 106x« - TOx^ by Iz^ - 5x- + 3. 58. 12 - 38x + 82x2 _ 1 x^j/ + x^^/^ - xy^ + 2/^ 59. x^ + 1/5 by X* 60. / + a6 + xy. 61. ab (x- + j/2) + xi/(a2 + 6-) by ax + by. 62. X* + (262 _ „2)^2 + j4 ijy x^ + ax + b\ 54. (jx^ 56. 2x2 82. The process may be shortened by the in smut; cases iise of brackets, as in the I'oUowing Example. -¥b3? i-l)x2-(m-l)x+l. — XV. Divide - c) x2 - (/> (/ + 7/1 + 11) 1/2 + (/,rt 1. X* - (a* - 2. y^ - 3. X* - (m. (r 4. u) 1/ r- - -ax + c.
Elementary Algebra by J. Hamblin Smith
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