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 UC-NRLF 
 
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IN MEMORIAM 
 FLORIAN CAJORl 
 
 8061 '12 NVl IVJ 
 
 jiapuig 
 
Answers 
 
 TO 
 
 -EMENTARY AlGEEEA 
 
 DY 
 
 FLORIAN CAJORI 
 
 AND 
 
 LETITIA ODELL 
 
 Beat pork 
 
 THE MACMILLAN COMPANY 
 
 1916 
 
 A II rights reserved 
 

 ' »^' '.'., 
 
 
 http://www.archive.org/details/answerstoeiementOOcajor 
 
Answers 
 
 TO 
 
 Elementary ALd^EBRA 
 
 BT 
 
 FLORIAN CAJORI 
 
 AND 
 
 LETITIA ODELL 
 
 THE MACMILLAN COMPANY 
 1916 
 
 All rights reserved 
 
• . • • • * 
 
 ^ 
 
 
 Copjrright, 1916 
 By The Macmillan Compant 
 
 Set up and eleotrotyped. Publttbed March, 1915 
 
 CAJORl 
 
ANSWERS TO EXERCISES AND PROBLEMS 
 
 IN ELEMENTARY ALGEBRA BY 
 
 CAJORI AND ODELL 
 
 Page 3.-27. 22. 28. 14. 29. 27. 30. 121. 31. 29. 32. 4. 33. 25 
 34. 2V4. 35. 64. 36. 964. 37. 47. 38. 10. 39. 259. 40. 111. 41. 42. 
 42. 75. 43. 75. 44. 70. 
 
 Page 6.— 1. 17. 2. 98 lbs. 3. 467* mi. per hr. 4. 46 mi. per hr. 
 5. 20 hrs. 6. 33 ft. 8. 45, 30. 9. 80, 46. 10. $30, $6. 11. $84, $12. 
 12. $80, $44. 13. 5. 14. IVa oz. 15. 1184. 16. 7. 17. $6000, 1"; 
 $5000, 2"; $3000, 3". 18. $12,000, A^s; $4000, B^s; $8000, C's. 19. 9 oz. 
 20. 20. 21. 1.20 ft. 22. 19.71. 23. 6.674; 4.626. 
 
 Page 10.— 16. (1) 32. (2) 64. (3) 96. (4) 896. (5) 35. (6) 246. 
 (7)243. (8)73,255. (9)3. (10)1. (11)1. (12)6234. (13)139. (14)59. 
 (15) 243. 17. 4; 64; 2500; 5184; 1024; 324; 40,000. 18. 80; 970; 
 9960; 99,950. 19. V4; Va; 2; "A; "/le. 20. 0; 0. 
 
 Page 12.— 1. 17. 2. 137. 3. 18. 4. 21. 5. 24. 6. 50. 7. 70. 
 8. 0. 9. 240. 
 
 Page 13.-1. 0. 2. 10. 3. 27. 4. 93. S. 3. 6. 24. 7. 8. 8. 4. 
 
 Page 13.-1. V«. 2. 2. 3. 589. 4. V4. 5. 6V11. 6. 2V20. 7. 156. 
 8. 56. 9. 82. 10. 4. 11. Yes; No. 12. No; No. 
 
 Page 18.— 4. - 10. 5. 45. 6. 15. 7. - 70. 8. 80. 9. - 4. 
 10.45. 11.75; -45. 12.-20. 13.-10. 14.10. 15.-40. 
 16. 80. 17. 70. 18. - 65. 19. - 70. 20. - 20. 21. - 45. 22. - 2. 
 23. 20. 24. - 80. 25. - 95. 26. - 95. 
 
 Pages 20-22.— 1: $100. 2. $180. 3. 5 cts. 4. 19 ft. lower. 
 5. 8 in. higher. 6. 92 mi. 7. 38** above; 12^ belaw; 112° below; 162^ 
 below; 222° below. 8. 8000 ft. higher; 1000 ft. lower; 5600 ft. lower; 
 
 . 6900 ft. lower; 6100 ft. lower. 9. 51V7^ 10. - PA^ H. $140. 
 
 > 12. 33° 11' 30". 13. 1° 48' 30". 14. 3' 32V2". 16. 43850'. 17. 3 hrs. 
 18. 10 mi. per hr. 19. 249 lbs. upward. 
 
 Page 24.— 1. 14 daa. 2. 46 ft., 1840 cu. ft. 
 
 Page 25.— 1. 11. 2. 14. 3. - 48V7. 4. - 351. 5. 3. 6. 76iVi4. 
 7. 12. 8. - 22. 9. 67. 
 
 3 
 
 915799 
 
4 ANSWERS. 
 
 Pages 26-27.— 1. 15o. 2. - 3c. 3. 5x + 12y + 5z. 4. 6a;. 
 
 5. 14a; + lOy, 6. 15c - 6d + 39c. 7. - 8a + 356 + 4e. 
 
 8. 14(a + 6). 9. - 7a^h^ - 2a¥ + 7ab^c. 10. 9fg - Sgh, 
 11. 5a H- 9b + 10c. 12. - 9aa;. 13. 3mn. 14. - 18A;Z. 15. - 5ac 
 
 - 36c - 9cdJ. 16. 55s^ - 9ty, 17. 10a - x. 
 
 Pages 27-28.— 1. lloc^ + 362c - Gc^ + 7ac. 2. 3a2 + 962 + 3^2. 
 
 3. 22a; - 2/ + 5xy. 4. 12a; - 7?/ - 142 + 7w " Sv. 5. 4a - 6 + 6c. 
 
 6. 5a + 86 + 4c. 7. 2a + 36 + 14c - 6rf + 3/. 8. 4a«6 + lla63 - lla6. 
 
 9. - a - 26 + 5c + d + 4e. 10. 7a; + ISy - 132 + 5w + v. 
 11. - 7a; + 2!/ + 62. 12. 2a - 4d. 13. - 3m + 16n + 6p. 
 14. - 1?/ 4- 6(7 + 47^. 15. 36 + 2c - lid + 3e. 16. - 17a - 14r 
 
 - 22s. 17. 5a - 286 - c. 18. 4x + 2/ + z + 5ii; - a + 6 - 6c + 4d, 
 19. _ 2a - 26 - 30c. 20. - 4a + 216 + 31c. 21. 4a* - 8a. 
 22. 6, - 6, 3, 12, - 12, - 9, 9, - 10. 23. 4, 20, 21. 24. 4, 9, 1, 100, 36. 
 25. - 60, 120, + 180, - 60, - 600. 26. - 8, - 27, - 1, 1000, 216, 
 8, - 1000. 27. - 4, 4000, - 3000, - 1000, 1000. 
 
 Page 29.-2. 3a;2 - 4a; - y. 3. 3a;2 + 5a; - Wy, 4. a;^ - 2a? - 15y. 
 5. 5a2 + 5a - 26. 6. 5a2 + a - 6. 7. ~ 7a2 + 29a + 146. 
 
 8. 3a3 + 562. 9. 5^3 + 263. 10. - a^ - 46*. 
 
 Pages 30-31.— 1. 4a + 5 - 4c. 2. - 2c - Sd. 3. a + 36 + 3c. 
 
 4. - a + 6 - 7c. 5. - 4n. 6. 3(f - 7e - 2/ + 6^^. 7. - 162 + 12m 
 
 - n - 3r - 5< + 92/. 8. 14a; + Qy + w. 9. - 14a + 56. 10. - 4r. 
 11. 6c - 4d - 6 + 3/. 12. 4a - 26 - c + 4d + c. 13. 4a + 26 - 2c. 
 14. - 4a + 36 - 5c. 15. 6n. 16. - llw - 2n + 4p. 
 
 Pages 31-32. — 1. x + (a + h — c + d) -\- y + i" m + n — s), 2. 2a; 
 
 - (~ 3a + 46 - 5c) - ^ - (6/c - 8Z - 7/ + 4g). 3. (3a + 2w? - 3c) 
 + a; + (~ 4r + 50 + 2/ + (5^ - 6w? + 7i) - a; 4- (a + 6). 4. - (9m 
 
 - 8i + 7w) + 62/ - (- 5i + 4r - 3e) + a;^ - (- 2w - 3a). 5. Sy + 
 (- c + 3a) - 2a; + (46 - 2d). 6. - (56) - a; + 31/ - (4c - 5d). 
 
 7. (- 5m + 6n) + 7x + (- 3p) - 42/. 8. Sy - (3c - 26 + 5a) + 5a;. 
 
 Page 36.— 1. 4. 2. 5. 3. - 2. 4. 6. 5. 6V2. 6. - 5. 7. 72/3. 
 
 8. - IV3. 9. 2. 10. - 20. 11. Vs. 12. - 60. 13. (a - 6)/2. 
 14. a - 6 -. c. 15. (c - 6)/2a. 16. (a + 6)/6. 17. a - 6. 18. 1/a. 
 19. 13. 20. (3c - 26)/a. 
 
 Page 37.— 1. - 22. 2. P/e. 3. - "/s. 4. 27V3. 5. 60. 6. 4. 
 
 Pages 37-40.— 1. 18 ft.; 8 ft. 2. 70 - 2w;; (70 - 1)12. 3. 180 ft.; 
 60 ft. 4. 70 yds. 5. 70 lbs.; 30 lbs. 6. 25V7 lbs. 7. 66Vs lbs.; 33 Vs lbs. 
 8. 126; 80. 9. 258; - 42. 10. I2V2; - I2V2. H. 20; - 4. 
 13. 22 min. 14. SVa min. IS. 8 dimes; 11 nickels. 16. 9 dimes; 
 
ANSWERS. 5 
 
 7 quarters. 17. 24 nickels; 79 pennies. 18. 7 dimes; 7 quarters. 
 
 19. 45°; - 10^ 20. 48°. 21. $437272. 22. $1500 at 6%; $1200 at 5%. 
 23. $3000 at 6%; $2000 at 7%. 24. James 54 words; John 108 words. 
 25.46; 35. 26. 3a/2; (5a + 26)/2. 27. (a + 6)/2; (a - 6)/2. 
 
 28. c/2; ~ c/2. 29. a dimes; b quarters. 30. 2T + t. 31. (3D + d)/2. 
 32. Father $4a/5; son $a/5. 33. (p + 2(?)/4; (p - 25)/4. 34. P/8; 3P/8. 
 35. 12; 13. 36. 24, 25, 26. 37. (s - 3)/3; s/3; (s + 3)/3. 38. 50; 52. 
 
 Pages 42-43.— 1. 6a^y + Sexy^ + ISxyz - 15t^X2/. 2. lOa^fec - 20ah^c 
 + 10a6c2e - 40abcd - lOahce. 3. Ox^j/^z^ + 3Qxyh^ - 45x^2/323 - 
 
 ISx^y^z, 4. - 6mn'o2 - lOn^o^ - Sn^o^ + lOn^o^p. 5. - 35 + 14o 
 - 146 + 21c - 28e. 6. - 4m + lOn^ + 120 - lOp. 7. ^aJ^hcd - 
 
 ^ux 
 
 .3 
 
 4ab^cd - 8a6c*d - 12ahcd*, 8. - ISafea;^ - Qax* + 16a<ix' - 2a/i 
 
 + 2agx\ 9. 12a - 186 - 24c -|- SOd, 10. - 10a; + 5qy - 152. 
 
 11. 72. 
 
 Pages 45^6.-1. x^ + 3a; + 2. 2. 2a;« + 7a; + 3. 3. 2a^ - 7x + 3. 
 4. 5x3 4. 21x2 + 6a; + 8. 5. - Oa;^ + 20x2 - 4x - 6. 6. 2/* - 7y^ 
 + 10^ + 42/ - 20. 7. 2/« - 2/5 - ^< - 2/2 + 2/ + 1. 8. 2^ - ^2 « -^ 
 + 1. 9. y* - 7y^ + 132/^ - 16^ + 5. 10. - 22^ - 22' + I222 - 2O2 
 
 - 60. 11. 6x6 _ 9a;3 4. 15a. ^ 2x*y - 3x22/ + St/. 12. 5x« + 9x» 
 + 6x2 4 2x. 13. 626 - 422^ - 22 4 7. 14. 2x3 4. 2^2 - 3x + 2. 
 15. x3 - V3X2 4. 10/33. _ 1. 15. 26 _ 1, 17. 33.3 _ a;2 _ 63. 4 4^ 
 
 18. - 2« + 8z3 - 1922 + 82 + 12. 19. - 32/5 + 15y^ + IQy^ + lly^ + 
 7y - 6. 20. 8x« + lOx^ - x^ - 24x3 - 9x2 4. 6x + 10. 21. 2x« + 5x« 
 
 - 7x< - 9x3 4. 5a;2 - 8x 4- 12. 22. 15x2 - xy + 2x2 + 15x - 2y^ - 3^2 
 + 52/ - 2* + 52. 23. 2a2 + ac - 262 4. 55^ - 3c2. 24. x* + x^y + 2x3 
 4- 2x22/ - 2x22/2 + 2x2/2 + x2 + xy, 25. x3 + x^y + x2/2 + x22 + X22 + 
 2/3 + y^z + 2/2^ + 2^- 26. a2 - 2a6 + 6a/ - 4a^ + e2 - 6e/ + 4e^ + 9/2 
 
 - 12fg + 4^2. 27. a2 + 2a6 - 2ac + 2ad + 2ae + 62 - 26c + 2bd + 
 26e + c2 - 2c(i - 2ce + J2 + 2c?6 -f eK 28. a* + 2a36 - 2a262 - 2a63 
 + 6*. 29. x3 - 6x2?/ -I- 12x2/2 - SyK 30. x3 - Sx^y + 3x2/2 - y^ + Sx^z 
 
 - 6x^2 + Sy^z + 3x22 _ 3^,22 + 23. 31. a3 - 3a26 + 3a62 _ 53 _ 3^2^ 
 4- 6a6c - 362c + 3ac2 «. 35^2 - c\ 
 
 Pages 46-47.-2. - 5. 3. - Vs. 4. - Vt. S. - 'A. 6. 5. 7. 11. 
 
 8. - 5. 9. - 13. 10. - 5. 11. 2/6. 12. - 2. 13. V19. 14. Vu. 
 15. - «V6. 16. - V2. 17. - Vi4. 18. - 7. 19. 5. 20. Vs. 
 
 ^n i -31a368c-2 ^ -- 5x^2^ , 69m3n-3o-« 
 Page 50.~1. ^ . 2. — g — . 3. g . 
 
 A - 56"2c-i(^'4g3 - pr2 18c8 ^ 16?«m^ . . . . 
 
 4. g . 5.-2^. ^'ZrmH^' ^•■49i;r- 8. 7aft. 
 
 9. IV/sxyin. 10. 143/5 nV in. 11. Z^I^-^cH. 12. 25x22/'. 
 
ANSWERS. 
 
 Page 51.-1. ~. 
 
 2. 
 
 17at*w 
 12 • 
 
 4. 
 
 7. 
 
 12 
 
 -5c» 
 
 8. 
 
 3M 
 
 c*y^2' 
 
 4a2e= 
 
 30;t*t^to^ 
 7xy^z 
 
 Page 53.— 1. 
 
 
 X 
 
 3w; * 
 
 13. 
 
 5d^y 
 2ax ' 
 
 14. 
 
 10. 
 
 3no» ' 
 
 5 ^' 
 11. 
 
 ' 21m • 
 ~ 16a^b^c*dh 
 f9 
 
 Sa^dehH^ 
 
 7mo^ 
 
 - 117dg*x*yh 
 124fh* 
 
 • h^cy ' -2QkH*p' 
 
 Page 54.— 1. 4x - 32^. 2. 4a + 2. 3. 3 - 4m. 4. be - 4(f/3. 
 
 5. 1 + 2/ii. 6. 2 - xz'. 7. 3a;V2 ~ 2/* 4- 2. 8. 3r + 4 ~ 2/r. 
 9. 4/3^» - 5/3xy - 4/3. 10. 3/4 + 5zV4 + 7wj/4. 11. 5 + 6ac - 8a. 
 
 12. - c + 4e/d - ce2. 13. ~ 5/3 + 2xy - yK 14. - 3/2 + ab^ - 2(ib^c\ 
 Page 56.— 1. a; + 1. 2. y + 2. 3. x + 2. 4. 2 - 2. 5. a;^ - a; + 1. 
 
 6. w^ -w + h 8. c2 + c + 1. 8. x^ + 2x^ + 4x + 8. 9. 6x^ + 7x« 
 -Sx + 30. 10. 5x3 _ ga;2 4. 9^ 4. 2. IIZ 2/* - y' - 2/ + 1. 12. a + 6 
 
 13. X — y. 14. X + y- 15. X — y, 16. m^ — mn -^ n^. 17. m* -f mn 
 * + nK 18. x* + x'2/ + x^y^ + X2/' + y*, 19. a^ 4- a'b^ + b*, 
 
 20. c' + dK 21. a^ - b». 22. x^ + x*y + a;V + x^y' + a;?/* -f y^ 
 23. 
 
 x* — x^y + a;22/2 — x?/^ + 2/*. 
 
 949 
 
 Page 57.-1. x^ + llx -f 106 + ~^£^ . 2. 2/^ - 42/ + 1 + ^^. 
 
 4. w« - w« + tr» - 1 + ■ ^ 
 
 28 + 4z2 
 
 M- 
 
 -212 + 5 
 
 22—42 
 
 3a2 + 16a - 10 
 
 7. r 
 
 12 , 
 
 a^ -7 
 r8 + H - 1 + 
 
 6* m' — 5m 
 
 uj2-f 1 • 
 Q , - m* + 9m + 16 
 
 r* + l' 
 
 8. «" -H 2s« + 45 + 
 
 8g ~ 1 
 fi'' ~2 ' 
 
 - SVt. S. - 7. 6. - 14. 
 
 11. 3(c - d)/4. 12. am/n. 
 
 16. - 5V7. 17. - 14. 
 
 21. 5r5/34. 
 
 Page 59.-1. 46. 2. 3IV3. 3. 2V3. 4. 
 
 7. 3o. 8. 3mn. 9. 2c. 10. I2V2. 
 
 13. mi/20. 14. rs/- 6. 15. 3IV3. 
 
 18. - 3.125 mn. 19. 13Vio7. 20. am/- n. 
 
 Pages 60-63.— 4. 92; 115. 5. -75; -200. 6. 62; -279. 
 
 7. - 38; 95. 8. $300; $350. 9. $4480. 10. 7 yrs. V2 mo. 11. 120 ft. 
 12. 180 ft. 14. 15,750 ft. 15. I28V7 cu. ft. cement; 2577? cu. ft. sand; 
 5UV7 cu. ft. gravel. 16. 26Vi7 cu. ft. cement; 66 Vn cu. ft. sand; 132 Vn 
 cu. ft. gravel. 17. A, $20777; B, $36272; C, $155Vi4. 18. 16. 
 
 19. Tea, 75c; Coffee, 50c; Butter, 30c. 
 
 Page 65.-2. 16?. .3. Between 11 A.M. and Noon. 4. 18^ 
 
 Pages 72-76.-1. 2Vii Kg., 37ii Kg., 47ii Kg; 46.2 lbs., 37.4 lbs.; 
 28.6 lbs. 2. 12.1 yds., 9.35 yds., 7.15 yds., 4.4 yds. 5. 86** F., 77** F., 
 
ANSWERS. 7 
 
 62V6'* F., 32** F., 14** F., - 4** F. 6. 262/8** C, I8V3** C, IIV9** C, 0^ C, 
 - 9V»** C, - 13V3** C, - im C, - 19V»^ C. 8. $8V8, SUVs, S14Ve, 
 $20, $23 Vs, S26V8. 9. S6, $18, $24, $27V6, $30. 11, $10.64, $15.80, 
 $26.35, $39.52. 12. $94,875, $75.90, $28.46. 
 
 Pages 77-78.— 1. 12. 2. 1. 3. Vs. 4. 24. 5. 14. 6. 1. 7. 12. 
 8. 6. 9. 3. 10. 10. 11. 2. 12. 5. 13. 6. . 14. 3. IS. 41. 16. V2. 
 
 17. 18. 18. 6. 19. 3. 20. 5. 
 
 Pages 78-83.— 1. 24. 2. 14, 15. 3. 9, 15. 4. 45, 3. 5. 7. 
 
 6. 15 in., 20 in. 7. 108 sq. in. 8. 7 ft., 2 ft. 9. 36 sq. ft. 10. 25, 26. 
 11. 24, 26, 28. 12. 15, 16, 17; 3 times; yes. 13. 22, 24, 25, 26. 
 14. 15 yrs. 15. 50 jrrs., 25 yrs. 16. 42 yrs. 17. 45 yrs., 15 yrs. 
 
 18. 15 yrs. 19. $150. 20. 50, 2c; 75, Ic. 21. 46V3 mi. by trolley; 
 68V8 mi. by train. 22. 7, 5c; 5, 25c. 23. 12 quarters, 15 halves. 
 24. 2 nickels, 16 quarters, 12 dimes. 25. 1", 60; 2", 50; 3", 40. 26. 15. 
 27. 500 mi. 28. 21 mi. 29. $4800. 30. $6550. 31. 4V2 yrs. 32. 4%. 
 33. $5800. 34. $400. 35. $3000 @ 51/2%; $680 @ 6%. 36. 9V2 mills. 
 37. 8V2 mills. 38. 6V4 mills. 39. 6V2 mills. 40. VU mills. 
 41. VU mills. 42. 7V2 mills. 43. $7353.54. 44. $3005.05. 
 45. $9747.74. 46. ^30,050.51. 47. $17,570. 48. 17,545. 
 49. $22,000. 50. $34,000. 51. $45,500. 52. $52,000. 53. 3V2 doz. 
 54. 9 hrs., 90 mi., 108 mi. 55. 3600. 56. 8.4 in. 57. 88V2 mi. 
 58. 144 sq. yd. 
 
 Pages 93-94.-1. 4(a - 2). 2. x\l - x), 3. 3a(6 - 2c). 
 
 4. 2x2(2/ - 3z). 5. a\h + c - d). 6. 2mhi{l - 3n + 4n2). 
 
 7. 5aH3a2 - 2a - 5). 8. 8c2(2c + d - 8c*d2). 9. ^{^ ^ ^ -\- x^ ■\- x^). 
 10. 6aS(2a~ 4a2 + 1). 11. x{x + 22/-1 - z). 12. 9dK2d^- 9d«+ 3 - d). 
 13. 17aH2/* - 2a2/'» + 4). 14. Zxyz{x + 2/ + 2). 15. llmK^n^ - 5n + 6r). 
 16. a^h^c\ab - ac ■\- he), 17. 2bcHK^ -f 4d - 6c). 18. hgh(15h^h 
 + Ugh -bg - 6). 19. a"(6 - c - d). 20. 2aj«(l - 36 + 4c). 
 
 21. 3a«6»c(l - 3(i + 2e). 22. y^^(c - d + g). 23. 6a*6»(l + 2a - Za^), 
 24. 22/*(4x» - 2 - x«2«). 
 
 Page 95.— 1. {x - y){a + h). 2. (x + 2y){a - &). 3. (c - aXx + y), 
 4. (c - d)& - 2). 5. (3c + d){a - 6 -f c). 6. (a + x)(- 2 + a - e). 
 7. (a - c)(6S- c). 8. (x - 2/)(r + s - 0- 9. (x - 2/)(a - 6). 
 
 10. (a; - 2/)(3 - d). 11. (c + d){a ~ 6). 12. (1/ - b)(x - a). 
 
 13. (d -f 3)(c - 2). 14. (3s + 2)(2r - 3). 15. (y + l)(y^ + 1). 
 
 16. (a - l)(a + 6). 17. (x - 2i/)(66 + 25c). 18. fe(3 - 5y^)(l - 2y), 
 
 19. (7r - 20(7o + 36). 20. (1 + a)(l -f 6). 21. (a + b)(x + y -^ z). 
 
 22. (x - l)(a - 6 - c). 23. (i - y)(a + 26 + c). 24. (a - 6 -{- c) 
 ' (2 + X + y). -. 
 
8 ANSWERS. 
 
 Page 96.— 1. (m + n)K 2. (o« - 2b)2. 3. (a* - Sb*)*. 4. (x 4- 12)2. 
 5. (63 + 4)2. 6. y + 8)2. 7. (2/ - Va)*. 8. (VsX + 1/4)2. 9. (6a - 6«)2. 
 
 10. (lie* - 62). 11. (Sy 4. 1)2. 12. (10 + hy. (13. (3u? - 3)2. 
 14. (1 - 136)2. 15. (5 + 4a)2. 16. (3c + 9^^68)2. 17. (4n - 7p)2. 
 18. {151 - 42/)2. IP. (2m + 16w)2. 20. (15s - 2^*^)2. 21. (a-\'h- 3)2. 
 22. [{x - yy + 4]2. 23. [6(r - s) - 5]K 24. [3(a + 6) - (c + d)]2. 
 
 25. [2 - 3(a - x)]K 26. (x + 1/ - 2)2. 27. {c + d + e)K 
 28. (a - 6 + 2)2. 29. (2w -f n + 1)2. 30. (g + 3/i + 1)2. 
 
 Page 97.-— 1. {x + y){x - y), 2. (a + 3)(a - 3). 3. (1 -|- 6)(1 - 6). 
 4. (2 -f m2)(2 - m2). 5. (2/» -|- 5)(2/» - 5). 6. (8c + z)(8c - z). 
 
 7. (5c3 + 7d2)(5c8 - 7^2). 8. (9 + lla;«)(9 - llx»). 
 
 9. (3r + 40 (3r - 40- 10. (lOpg + 9w^)(10p? - 9i^). 
 
 11. (6x5 + 72/6) (6x8 - 72/6). 12. (12w; + bx^){\2w + 5a;2). 
 13. {h 4- 13) (A - 13). 14. (2a + l)(2a - 1). 15. (4a6 + 5c)(4a6 - 5c). 
 16. (15? + 122) (15g - 122). 17. {lOw + 16t;2)(10w; - 16i;2). 
 18. (3x2/ + ll)(3a;2/ - 11). 19. (7c3 + 8<*)(7c» - 8^*). 
 20. (17a6c + 5(i)(17a6c - 5d). 21. {x -^ y ■\- l){x -^ y - 1). 
 22. (a 4- 36 + c){a + 36 - c). 23. {x - 2y -\- z){x ~ 2?/ - 2). 
 24. (m + 6w + 2r)(m + 6n - 2r). 25. (7d - r + 5s)(7(i - r - 5s). 
 
 26. (a + 6 + 2c)(a + 6 ~ 2c). 27. (x - y -\- z){x - y - z). 
 28. (c - 3d + e)(c - 3rf - e). 29. (6 - 9 + 7s)(6 - 9 - 75). 
 30. ((i - 6 + 5t)(d - 6 - 50. 31. (1 + o 4- 6)(1 - a - 6). 
 32. (4 + a; - 2/)(4 - x + j/). 33. (3 + m - 3n)(3 - m + 3n). 
 34. (fc + A 4- 10)(A; -h" 10). 35. (a 4- 6 4- c){a - 6 - c). 
 36. (i + m - n)(« - m + n). 37. (7 4- c 4- 3(i)(7 - c - 3d). 
 38. (9p 4- 6g - l)(9p - 6g 4- 1). 39. (10s 4- 4/i 4- 2) (10s - 4h - 2). 
 41. (x 4- 22/ 4- w - n)(x 4" 22/ - m 4- w). 42. (3c - 3d 4- 2x - 22/) 
 (3c- 3d - 2x + 22/). 43. (8^1 4" 8Z 4- 7r - 7t){Sh 4- 8Z - 7r 4- 70- 
 44. (12m - 12x 4" Hw 4- ny){12m - 12x - llw - lly), 45. (62/- 62 
 4- Uw 4- 14x)(62/ - 62 - Uw - 14x). 46. (c + d + m - r){c 4- d 
 — m 4- 0« 
 
 Pages lOO-lOl.-l. (3x 4- 2)(2x + 1). 2. (3x 4- 5)(2x 4- 1). 
 
 5. (3x + l)(x4-2). 
 8. (8m - 15) (m - 2). 
 11. & - 2){2t - 5). 
 14. (62/ + 5)(5y-l). 
 17. (5m - 2) (3m 4- 4). 
 20. (3d + l)(2d - 5). 
 23. (3o - 6) (a 4- 46). 
 
 3. (12x - 5)(x 4- 1). 
 
 4. (7x + 4)(x4-l). 
 
 6. (5x4-7)(4x4-l). 
 
 7. (2a - l)(a - 13). 
 
 9. (56 -6) (26 -5) 
 
 10. (32/ - 5) (22/ - 7). 
 
 12. (3s - 2)(s 4- 5). 
 
 13. (8s 4- 3) (3s -1). 
 
 15. (4m 4- 3) (2m -7). 
 
 16. (3m + 2)(m - 1). 
 
 18. (6a- l)(3a + 2). 
 
 19. (6c - l)(c-f 6). 
 
 21. (11^ 4- i)(g ~ 2). 
 
 22. (2^4-5A)(y4-3/i). 
 
 24. (3a4-26)(a-36). 
 
 
ANSWERS. 9 
 
 Page 101.— 1. ix + y){z^ - xy -{- y^). 2. (a; - 2/)(x« + xy + y% 
 
 3. (m + l)(m2 - m + 1). 4. (m - l)(m2 + m + 1). 
 5. {ab + 2)(a262 - 2a6 + 4). 6. {cd - 3)(c2d2 + 3cd + 9). 
 7. (4a - l)(16a2 + 4a + 1). 8. (56 + 6) (2562 - 306 + 36). 
 
 9. {2g - 36) (4^2 ^ Qgh + g/^i), iq. (xy + 7)(xV - 7^2/ + 49). 
 11. {x^ + 2/')(x* - xV + 2/0. 12. (2a« - 62)(4a* + 2a262 + 6*). 
 13. (1 - 3a3)(l + 3a» + 9a«). 14. {m* + n*){m^ - m*n* + w«). 
 15. (3c« + l)(9cio - Sc^ + 1). 16. (2a'* - l)(4a«» + 2a» + 1). 
 17. (6«'» + c2")(6«'» - 63«c2» + c*«). 18. (x + y)(x^ - xy + y^){x^ - 
 xV + 2/'). 19. (4a - 56)(16a2 + 20a6 + 256^). 20. 27(2 - x«)(4 + 
 2x8 4. a.12). 
 
 Pages 102-103.— 1. a{a + 1)K 2. 2(x2 + 3)2. 3. y*{S - ^y^)K 
 
 4. 6(6 + 1)(6 - 1). 5. (x2 + 4)(x + 2)(x - 2). 6. (a +^7) (a ~ 1). 
 7. (a + 15)(a + 1). 8. (x - y)ia - 2). 9. (w - n)ia + 6)(a - 6). 
 
 10. (c + DHc - 1). 11. (x^ - 7)(x + l)(x2 - X + 1). 12. (fc2 - 8) 
 (fc + 3)(/b - 3). 13. (2 + x)(4 - 2x + x2)(2 - x)(4 + 2x + x*). 14. 
 {h - 7)(A2 - 2). 15. (9^12 + ]^2)(^h + /^)(3;i _ /;). 15. (^j _ ^Z + 2) 
 (x - 2/ - z). 17. (3m2 + 7)(m2 - 5). 18. (y - 4)(2/2 + 42/ + 16). 
 
 19. (L + 1/2)^ 20. (x + 2)2(x + 2). 21. (a + 6)». 
 22. 2(a - 7)(a2 - 5). 23. (a + 6 + 1)2. 24. (a - 6 + 3)(a - 6 - 3). 
 25. (c + a-6)(c-a + 6). 26. (1 + xO(l - x* + x*). 
 27. (r + 14)(r - 11). 28. (x + 21)(x - 10). 29. (a2 + 62)(a* - a262 
 + h*)(a + 6)(a2 - 06 + 62)(a - 6)(a2 + a6 + 6*). 30. (2s - l)(s - 2). 
 31. 7(a - 5)2. 32. 6(3 + 2x)(l - x). 33. (17w? - 9)(w? + 2). 
 34. (3x» + 5)(3x« ~ 5). 35. (a - c)(a + 26). 36. c^{c^ - 6)(c8 + 6c» 
 + 36). 37. (a + 26 — c)(a - 26 + c). 38. (a — m + n)(a — m — n). 
 39. 3(x - a)(x + 1). 40. (7c + 13) (c + 1). 41. (e + Sf)(e^ - Sef 
 + 64/2). 42. (62/ - 7z){y + 82). 43. (a - 66 + t)(a - 66 - 0- 
 44. (1 + 3x + 52/)(l - 3x - 5y). 45. (9c2 - 7d'Kc + d)(c - d). 
 46. (3m + 2»)(3m - 2n){7:i + n)(m - n). 47. (a + 6)(a - 6 - 1). 
 48. (a + 6)(a2 - a6 + 62 + a - 6). 49. (2a - 6 + 3c + 4d)(2a - 6 - 
 3c - M). 50. (x + 2/ - 3)(x + 2/ - 2). 51. ax2/(a2 + 62) (a + 6)(a - 
 6). 52. x'»(2x2» 4. i)(2x2» - 1). 53. (7a* - 66v)2. 54. (25x3 - SQy^) 
 (x - y){x^ + X2/ + ^2). 55. (x2 + Qy^){x' - 9x'y* + 81^^. 
 56. [Ur^iy - z) + 15s] [14r3(2/ - z) - 15s]. 57. (2x + 2/ + 1)^. 58. 
 (3c - 2e - 5)(d + 7). 59. (x2 + 2/2 - 2)(x + y)ix - 2/). 60. (72/ - 5z)K 
 
 Page 106.— 1. ±5. 2. ± 6. 3. 0, 4. 4. 0, a. 5. 5, 2. 6. 5, - 2. 
 7. 0, 7. 8. 0, 3. 9. - 9, 8. 10. a, a. 11. 0, V2. 12. 0, a/6. 13. dt a. 
 14. V2,2. 15. -V4,V3. 16. V6,V6. 17.2/5,3/6. 18. a, 6. 19. 0, a + 6. 
 
 20. c/3, a/2. 21. 0, 2, - 2. 22. 2, 2, - 2. 23. 0, 2, 1, 24. 0, 4, 5. 
 Pages 107-110.— 1. - 7, 6. 2. 7, - 2. 3. - 11, 10. 4. 29, 11. 
 
10 ANSWERS. 
 
 5. - 8, - 5; 6, 8. 7. 6 ft. 8. 3 in. 9. 7 persons; $12. 10. 2a: -fl; 
 odd. 11. 6, 7; - 7, - 6. 12. - 11, - 9; 9, 11. 13. 8 seats. 14. 3 in. 
 15. 10 ft. less. 16, 8 in. 17. 6 in. 18. 12 ft. 19. 7 ft., 10 ft. 
 20. 9 ft., 12 ft., 15 ft. 21. 216 sq. in. 22. 141.4 in. 23. 853V« sq. ft. 
 24. 10ft. 25. 15 in. 26. 9ft., 11 ft., 12ft. 27. 14 in. 28. 2828^7 sq.ft. 
 
 Page 111.— 1. 6o« -f 5a« - 19a* + 13a - 5. 2. 3a» + 2a* - 6a» 
 
 + 5a« - 14a + 6. 3. 6x* -f 7x» - 10x« + 17x - 20. 4. x* - y*. 
 
 5. 4a:» - IQx'^y + l%xy^ - ^y^, 6. x* + a:* + 1. 7. 1 - 3a + a* + 3a» 
 - a* - 2a^ + a\ 8. c« - 2c7 -f c« - 2c^ -f 4c* - 2c» + c« - 2c + 1. 
 9. x« - yK 10. - 18a« + 21a5 - 11a* + 5a» + 3a« - o + 1. 
 
 11. m8 + 3m5 - 11m* - 15w» + 50w2 - 36m + 8. 12. 15r^ - f^ + 
 35r* - 9r» + 21r» + 2r - 7. 13. a^ - 68. 14. x» - Zxyz + 2/» + «». 
 15. 8a:8 4. i0a;6 .. 63a;* + 27x« + 49a;* - 37x + 6. 
 
 Page 113.— 1. x2 - 7a; + 2. 2. 2a2 + 3a6 + 46*. 3. 2a* + 5o6 - 36«. 
 
 4. x* - a; + 3. 5. a - 6. 6. 5a* - 2a + 1. 7. r^ ^' r^ - 1. 
 
 8. a* + 06 + 6*. 9. X* + x^y + a;*2/* -f xj/' -f 2/*- 10. a* - 06 - oc 
 + 6* - 6c + c*. 11. x' + 3x* + 4x + 2. 12. x* -f x»2/ + xy^ -f |/«. 
 13. a» + 2a*6 + 2a62 + 6^ 14. a^ - a*6 - 06* + 6*. 15. 2y, 
 
 Pages 115-116.-1. a* - 2a + 1. 2. x* - 3x + 2. 3. c» -f 3c* - 4c - 1. 
 
 4. 2x* - 3x* - 6. 5. 5x3 _ 2x^y + 3x2/* - 22/*. 6. 3c*d - 3cd* - 2dK 
 7. mW - 3mwr - 4r2. 8. x* - x/3. 9. a/2 - 6/3 + 1. 10. 
 
 2x - 5 + l/2x. 
 
 r Pages 117-118.-1. 57. 2. 78. 3. 227. 4. 306. 5. 498. 
 
 6. 10.87. 7. 1005. 8. 3.24. 9. .0751. 10. 8.01. 11. .1234. 
 
 12. 38.2. 13. 20.506. 14. 2784.53. 15. 1.414. 16. 1.732. 17. 2.236. 
 18. .816. 19. .894. 20. .942. 
 
 Pages 122-123.— 1. 11.32 fr. 2. 16.98 fr. 3. 33.96 fr. 4. 31.13 fr. 
 
 5. 25.47 fr. 6. 19.81 fr. 7. $.883. 8. $1.76. 9. $2.64. 10. $3.52. 
 11. $4.41. 12. $4.76. 
 
 Page 127.-1. 7, 5. 2. 1, - 3. 3. 20, 10. 4. IVs, l*/8. 5. Vj, V4. 
 
 6. 0, 2. 7. Infinite no. of roots. 8. 3, 2. 9. Inconsistent. 10. 12, 13. 
 11. -4,-7. 12. - 8, 13. 
 
 Page 128.-1. 0, 2. 2. 12, 12. 3. 6, 20. 4. 15, 1. 5. 23, - 1. 
 6. - 3, 4. 7. V4, - Ve. 8. 13, 2. 9. V«, 1. 10- - 1, - V2. 
 
 11. Infinite no. of roots. 12. Inconsistent. 
 
 Page 129.— 1. 1, 2. 2. 8, 9. 
 6. 0, - V4. 7. 5, 1. 8. 34, 15. 
 
 12. 7, - 2. 13. + 6, + 3. 14. 
 
 3. 13, 25. 
 
 4. V4, 2. 
 
 5. 14, 6. 
 
 9. 14, 8. 
 
 10. 16, 23. 
 
 11. 10, 6. 
 
 - 20, - 30. 
 
 
 
ANSWERS. 11 
 
 P«e. 131-132.-1. --±-\ -^^ 2. ^^ Lr^. 
 
 3 £^_dbj^ en — dm . ahcd bed « d -h n c — m 
 
 ' o5 + (i ' a6 4- d ' ' dm -^ en' en -^ dm' 
 b — a — b — a 
 
 2c + 3d 2d -3c oc + ad be-bd 
 
 ~135~ • "• 2~~ • 2 • 
 ,. et(bm — aw) ab(o>n — hn) ,_ e 
 
 **• 6«-o» ' o« - 6« • "• 2x • 
 
 2^ 18. f.^. 19.^. 
 
 . AC 3608 
 ^** 360 ' C • 
 
 2. 2, 2. 3. Vi, - Vi. 4. »A, Va. 
 
 o 4-c y 3m -h2n 3m -f 2n 
 
 5 -I- d* 6c - ad • ^' 5m + an' 26 - 3a • 
 
 9 1 ^ 10 1 L 
 
 9a' 56 n' m 
 
 Pages 134-135.— 1. 37?, 0, 37?. 2. 7, - 7, 2. 3. Infinite no. of roots. 
 
 4. 5, 5, 5. 5. 3, - 2, - 2Vj. 6. 3, - 2, 6. 7. 4, 1, - 2. 8. 15, 10, 12. 
 
 9. 1, Va, V«. 10. -- V8, V2, 1. 11. V37, - Ve, - Vm. 12. .1, .2, .5, .3. 
 
 Pages 135-138.— 1. 41, 37. 2. 51, 25. 3. 28V2, I6V2. 4. 9Vi, 15V». 
 
 5. 12, 11. 6. 25, 47. 7. - 44, - 54. 8. 14, 12. 9. $85, $40. 
 
 10. $5750, $5500. 11, 46 yrs., 25 yrs. 12. 30c, 6c. 13. $1.25, 30c. 
 14. 27, 16. 15. Vs. 16. 6, 15, 8. 17. $1, $1.50, $1.75. 18. 35, 22. 
 19. $20. 20. A, $25; B $75. 21. V/i days. 22. A, 5V7 days; B, 13Vi. 
 days; C 40 days. 23. 15 boys; $4; $60. 24. 45. 25. Any number 
 in which the tens' digit exceeds the units' digit by 5. 26. 236. 27. A to 
 B, 50 mi. ; B to C, 90 mi. ; C to A, 60 mi. 28. 15 mi., 12 in. 29. 10 hrs., 
 50 mi. per hr., 500 mi. 30. $5000 @ 4% ; $7000 @ 3V2%. 31. A, $5000; 
 B, $3750. 32. $1050. 33. 88c; 28c. 
 
 Page 142.— 1. ± Vj V5. 3. rb 2. 4. =b VS. 5. ± V2. 6. ± Vlo! 
 
 7. ± V6. 8. ±3. 9. d:2V2'. 10. ± V16. 11. ±3. 
 
 12. 0, - 2.89. 13. 0, 1.5. 14. ± «/«. 15. ± 7*^55. 16. ± V.15. 
 17. 0, 8. 
 
12 ANSWERS. 
 
 Pages 144-147.— 1. 2, - 8. 2. 2, - 12. 3. •/», - '/a- 4- 'A, - 'A. 
 
 S. v.. - V,. 6. 3, - 'A. 8. - V. ± VIO. 9. 2^. 10. 2^5. 
 
 11. 5 ±2^ 12. ~^^^ . 13. V:o. - »V... 14. ^^• 
 
 15, Vn, - Vu. 16. 'A, - 2. 17. 0, «A. 18. 0, - 2. 19. ^ =^ "^^^ 
 
 4 
 
 M 6/ ^.jr „ - 7± Vi049 „ 6d:>S8i „ 1±_^. 
 20. Vii V5. 21. g^ . 22. 22 • 23. g 
 
 24. I±^^. 25. v.. -v.. 26.^1-=|^. 27. -7±V^. . 
 
 28. i^^. 29. ::iif^. 30. -^t^ . 31.2±>i: 
 
 — 4 o 10 
 
 32.V,.-1. 33. 'A. "A. 34. Zil^:^. 35. " ^'^ ^^"^ . 
 
 D 4 
 
 36.3^. 37.i*3^. 38. -V. 'A. 39.17.-27. 
 
 40.1V,, -v.. 41.3^. 42. «^^. 43.^-^. 
 
 45. ±3->S, ±2a5, ±2aV3, ± 5a6V2, ± 10x«a/35. 46. 2±2>S'. 
 
 47.3±2V7. 48.^1:!!?. 49.?^. SO. ^^. 
 
 51. 3 ±2^5: 53. L^p^ . 54. 1, - Vs. 55. L±^. 
 
 56. 5, - 4. 57. =b a/s: 58. 5, Vs. 59. 9, Vs. 60. "" ^ "^ f^^ ^ 
 61. ± VlO. 62. 6, 2. 
 
 Pages 147-150.— 2. 13, 11. 3. 16 in., 7 in. 4. ^Vs in., Vs in. 
 
 5. V2 ft., "/2 ft. 6. 3V2 ft., IOV2 ft. 7. 10 in. sq. 8. 13 in., 11 in. 
 9. 2V2 ft. 10. 4 in., 7 in. 11. 40 ft., 50 ft., 30 ft. 12. 6 + 3>/2 in., 
 3 4- 3>/Jin. 13. 59, 60; - 60, - 59. 14. 11 in., 16 in. 15. 27, - 7- 
 16. 44 books. 17. 28 days. 18. 2 in. 19. 5 in., 9 in., 4 in. 
 20. 7 ft., 27 ft. 21. 175, 176; - 176, - 175. 22. 32, 34; - 34, - 32. . 
 23. 27, 29; - 29, - 27. 24. 6 ft., 9 ft., 18 ft. 
 
 T»- iei o 1 8/ o -5:tVl30 . ^ ,, - 3 =t 2V6 
 Page 151. — 2. 1, Ve. 3. = . 4. 2, — Vs. 5. = . 
 
 7 o 
 
 6. 5±^. 7. i-^^. 8. 18±V354. 9.-5^2^7. 
 
 10.1, -Vs. lL16d:2V55. 12. ^Q^=^/^^ 
 
ANSWERS. 13 
 
 Pages 151-152.— 1. 9,-2. 2. 3 ± >ff7. 3. - 16, - 2. 
 
 I/O « ~5=fc V35 ^ --25^ Vi45 „ ^ . 
 
 4. - Vj, - 2. 5. 2 • ^- 15 • ^- ^' ^' 
 
 8. 14, - 10. 9. 3, - 6. 10. 0, - 7. 11. 6, -IS. 12. 3, 2. 
 
 13. - 15, 3. l4.-l-±^}^ . 15. 1/,. 16. 5, 3. 17. 2, - V*. 
 V 18. 11. 10. Va, - 2. 20. Vi8. 21. V2, Vs. 22. Va- 23. 5, - "/t. 
 
 24. V6, - V2. 25. 1 ± V2, 26. '^ ^ ^ ' ^^' =*= '/'^• 
 
 ^ 28 "^=^^ 29 ^^^ 30 ^^^ . 
 
 Page 153.— 1. "" ^ "t ^^^ . 2. - 1 d: V=^. 3. 1 d= 2>P1. 
 
 -3:i: V~^ 
 
 4 • 
 
 Page 156.— 1. 1, 25; 2, - 10. 2. 3, «/»; 2, - "/,. 3. 10, - 6; 
 
 20, "A. 4. - 45, 10; «V2, 10. 5. Vs, "/21; 1, - Vt. 6. 0, - Vs; 
 
 0, !«/•. 7. - 3, - «A2; 3, - Vi. 8. - 2, - "A; 3, - 8. 9. 8, 4; 
 
 3, - 1. 10. 5, 1; - 10, -2. 
 
 Page 157.— 2. 3, - "Ao; 30, 'sVio. 3. Vs; Va. 4. 30, 50. 
 
 Pages 158-160.— 2. 12, - 3; - 3, 12. 3. 12, 11; 11, 12. 4. V2, Va; 
 Va, V2. 5. I2V2, - IV2; IV2, - I2V2. 6. 7, - 6; 5, - 8. 7. - 6, 5. 
 8. V2, - V3; - Vs, V2. 9. 3, 2. 11. 3, - 2; 2, - 3. 12. - Vs, + 4; 
 - "A, + 5. 13. 5, - "A; 2, - "A. 14. »Vi3, 7; "As, 8. 15. - 15, 5; 
 15, 5. 16. 1. 15; 3, - 11. 17. 2, 6; 4, 0. 18. 13, - 3; 18, 2. 
 
 19. 10, - 14; 11, - 5. 20. 1, Vis; 1, - "As. 21. ^so/.^, iQ; - 7o/^,, 10. 
 22. "V26, 2; - *^U, 3. 23. ± 11; d= 11. 24. ± 1; =F 1. 25. 5, - 9; 
 
 4, - 10. 26. 2, - 8; 7, 13. 
 
 Pages 162-163.-1. No; No. 3. 2". 5. "/89. 6. x/y. 7. x/my. 
 
 8.1. 9.^i^. 10.^4±i^. 11. v.. 12.?^^-^ 13.?. 
 
 X — y 2x{x — 1) X y 
 
 ...-,. .5.—,. .,.1^;. .7.||±|. 
 
 ,s,^+»L. „.-.,,. 20.. + ,. 21.1+5. 2j.e<!^:i). 
 
 — X — y o d 
 
 23.-^. 24. ?^^ 25.?^. 2«.-^. 27.-5. 
 
 jre + 3 y — 4 4 a — y 
 
 28 ^ 29 ° + ^ 30 JL^Z±- 31 y-2^ 32 ^-TJ? 
 
14 ANSWERS. 
 
 Pages 165-l«».-3.^. 4. f . 5.g'. 6. 5^>. 
 
 7.2x(l-y). 8.1. 9.^^^'. 10.%. 11. ^^' + ^ + ^> . 
 ,2.V. 13. ''^^'-^ + ^'> . 14.4(x-j,). 15.Wl£>. 
 
 16 ? 17 'g 18 3a;» 12x + y 
 
 » ' 2j/(l -2x+ 4x«) • *"• j/»(l +3y + 9y^) * *"• » + j, • 
 
 20. .^^ + ^ , . 21.(2x + 3).. 22.-f±|,. 23. <^1^ . 
 x^ -{-xy — y^ x(x 4-5) x* ^ 
 
 24. (x + yKx - l)(x2 - X + 1). 
 Page 167.--^ 14^:^^ ^ m« - n« ^ m 4- 1 
 
 72/ + 5a; * * m* + n» * 2w - 1 * 
 
 ^• I2(4mn+l) - «' "^ • '•"/'• ^»- "/'" "' t^-a • 
 
 g« + a; - 4 -. 2 4-1/ -g 
 
 lib* r = • X<9* , • 
 
 a;* — 7 X -{- y 
 
 Pages 168-169.-1. a*. 2. xj/. 3. 5a*. 4. 6a'^bc. 5. o. 6. a; — |/. 
 
 7. a;« 4- 2/*. 8. a 4- &. 9. x - y, 10. a; - 1. 11. 2(a 4- 1). 
 12. a 4- &. 13. X - y, 14. x - 2. 15. a; 4- 2/. 16. m 4- 3. 
 17. a - 1. 18. o2(a 4- 2). 19. (x 4- yy(x - 2/)^ 20. r - 2s. 
 
 Pages 169-170.— 1. xyz, 2. a^hK 3. fe'c^d*. 4. 70 cde. 
 
 5. a*(a 4- 1). 6. a{a 4- l)(a - 1). 7. cd(c + <i). 8. ab(a 4- 6) (a - 6). 
 
 9. (a 4- 2)(a ~ 2)(a 4- 3). 10. (x ~ 2/)Ha; 4- 2/)'. 11. (a - b^ia 4- 
 6)(a* + o& 4- fe^). 12. (m 4- n)2(w2 4- n*). 13. 3(w - w)(m» 4- nm 
 4- n«). 14. (x 4- 2)(x 4- 3)^ 15. (a ~ 4)(a - 2) (a 4- 3). 16. (1 4- 
 x)(l-x)(14-a;4-a;*). 17. x2/2(x4-2/)(a: - 2/). 18. (x -3)(x4-3)(x4- 7). 
 19. (a 4- l)(a - l)(a2 4- 1). 20. (x - 2ynx 4- 42/) (x 4- 2/). 
 
 Page 170.— 1. 12; 72. 2. 48; 288. 3. 49; 294. 4. 36; 7560. 
 5. 2x2/; 40x62/»2«. 6. 25; 300ao»d^ 7. a; 3a(a - 6). 
 
 8. 4ax; ^ax^a^ - x«). 9. x 4- 3; (x 4- 3)(x - 3)(x 4* 2). 
 
 10. 6 4- a;; ab{b + x). 11. x 4- 2/5 (^ + 2/)*(2J — y)i^^ — xy 4- 2/*). 
 12. 3 - a; 4(3 ~ a)*(9 4- 3a 4- a*). 13. a - 26; a(a - 26) (a 4- 36) (a , 
 - 46). 14. c+d; (c 4- ci)(c - 2d)(?n - n). 
 
 Pages 171-172.-1. -/.. 2. ?ii±A^ 3. 452/+ 25x 4-4 
 
 , 10a*6 - 2a6« 4- 3a*6« ^ x + 3y ^ x - 82/ 
 
 75 • 15xV 
 
 f 32/ g x-32/ 
 
 50 • "• 10 • ^' {x4-2/)(iC'-l/)' 
 
 + x-y g gi 4- X2/ - 1 p^ y ^^ 1 
 
 (x - 2/)' * * (x 4- 2/)' ' ' (« 4- 2/)(ic - 1/) * ' ^' 
 
ANSWERS. 15 
 
 11 5x« -> 2xv -f 5y« 2x 2y 
 
 6(x + y)(x - 2/) • "• (X + yKx - y) ' ^^* (x + y)(x-y)* 
 
 14. -^-±^. 15. --i:2x^+J^. 16, 31 
 
 a;(m - x) • * x(x + y)(a; - j/) * 12(2a; + 6) 
 
 !y - 1) • 
 
 2o + 26 + 2c 
 (a + 6)(6 + c)(a + c)^ 
 
 17 y + ^ 18 i2£jLl ig ^ 20 
 
 ^^•30(3y~l)- ^®-35(x4.1)- ^^- sT ^' ^^- ^' 
 
 21. 
 
 Pages 173-174.— 1. IVt. 2. 3V«. 3. P/s. 4. 5. 5. V/v. 6. 6. 
 
 /«. 12. V7. 
 33 db V409 
 
 7. IVw. 8. ^ . 9. 0, 9. 10. - IV26. 11. - "/m. 12. V7. 
 
 13. 1. 14. IVe. 15. - 5. 16. 0, - V2. 17. 3, V3. 18. 
 
 19. IVfi. 20. 3, - 7. 21. - 4 rfc V5. 22. 0, 5. 23. 6, - 3. 
 24. 2, - 1. 25. - 6, - 6. 26. 2, 2. 27. 11, "A*. 28. IVj. 
 
 29. ^2V. 30.1^. 
 
 Pages 174-176.— 1. - 12, 6. 2. 182. 3. 17 yrs. 4. 30 yrs. 
 
 5. V». 6. 16 in. by 12 in. 7. 4 in. by 6 in. 8. 35, 49. 9. 120. 
 
 10. 40 mi., 50 mi. 11. 4 hrs. 12. S^h hrs. 13. 13Vs hrs. 14. 24. 
 
 15. 6000 tons. 16. $12,000. 17. 5V2yrs. 18. 6 games. 19. 160 cu. ft. 
 
 Page 181.-1. ^aT 2. V5«. 3. ^xV- 4. V7a. 5. 2^5x. 
 
 6. 2\^a2. 7. ^4a2. S.2<x^ly, 9.6^la^^ly. 10. 7^(3m)«I 
 
 11. Va6. 12. 3^5. 13. <lix + y)\ 14. 4\'(c ~ d)«. IS. S^o^Vx^. 
 
 16. a*\^6^. 
 
 Pages 182-183.— 1. V«. 2. 8. 3. 5. 4. V2. 5. 27. 6. 9. 7. 5. 
 8. V4. 9. 42. 10. - 1V4. 11. 9. 12. V,. 13. - 'A- 14. V». 15. V«. 
 
 16. Vs. 17. 25. 18. Vt. 19. 9. 20. 1. 21. |. ' 22. l2yK 
 
 23.6X2,'.. 24. -|i. 25.?4-\ 26. ^t^ . 
 16a2 o5 6 — a 
 
 Pages 184-185.— 1. 2V2. 2. 2^3^ 3. 2V5^ 4. 2V6; 5. 2V7l 
 6. 2VIO. 7. 6Vri. 8. 12^. 9. - ISVS*. 10. 20V3; 11. 2Vl4. 
 
 12. 77. 13. -32ViO. 14. 10 VS^ 15. 15 Vs! 16. -OOVsI 
 
 17. 271/2. 18. 16V5^ 19. -2V3*. 20. w/sVs". 21. 2\^2; 
 22. 6^2. 23. 10\'2'. 24. 14^^71 25. 6^11. 26. 3^2l 
 27. 100^10. 28. 2.^ 29. 6<ls, 30. 14^10. 31. 2\^7". 32. x<x. 
 
16 ANSWERS. 
 
 33. c^-^c, 34. y'-^. 35. ac^. 36. hx^ly. 37. ir^4nm, 
 
 38. VaA/a; 39. VsVS". 40. V4Vi4. 41. Ve^^. 42. V«>/3l 
 
 43. Ve^. 44. VwVs". 45. Vs^^lS. 46. V2^T; 47. ^U^% 48. ^6: 
 
 4P. Vf^ii. 50. V8^45. 51. Vi. 52. ^aS". 53. -V^ 54. ^Vl 
 
 55. —r—^xTy. 56. -\'^. 57. Va;' - y*. 
 
 ic + y 2/ 
 
 m^n i— ; . _,^ 1 I £ 
 
 58. <m{m — n). 59. r Va — 6. 60. {x + 2/) Vx^ y. 
 
 m — n a — o 
 
 Page 186.— 1. - ^ 2. 7^5: 3. SVu. 4. 7<a. 5. (a + &)>/&: 
 
 6. V2^. 7. 8^. 8. V2V6. 9. - VibVIS. 10. ^^ V5. 
 
 11. 4>/5'. 12. 14 aS; 13. I5V7: 14. 0. 15. (a + 6 - Z)<b. 
 16. (2a-c4-2J>/a6. 17. ^'"^^"^ ■■Vi. 18. (a + 5) VSTT - 
 
 Va« - 6«. 19. ^^ + ^ - ^ V^. 20. (x - y - 2a;y) VJ+T- 
 
 mn 
 
 21. 9^2. 22. ^iM- W, 23. 5\'x"^=^. 24. i^JcT^. 
 
 Pages 187-188.— 1. 3 aS" - V2T - 2 >/§! 2. V35 + Vl5 - V55. 
 
 3. 6V3~- 6^l2 + V30. 4. 5^ - 8 V5 + 10. 5. - 27 V2 + 42. 
 
 6. 21 + 7->S - 3>/3 - VeT 7. 8^5 - V30 - 32 + 4V6: 
 
 8. - 48 - 7V5. 9. - 70. 10. 30. 11. - 5 + 2^42. 
 
 12. 10>S - 6VT5 - 4V70 - 10 + 3V3O + 4V35 - 2V1O + 6V3 + 4Vi4". 
 
 13. 3 4- "/3o>/30 - 1735 >/35 - iV42>/42. 14. {x -y)^xy+x^ + y<x. 
 15. - 3 - ^^12 + 2\'2 + a'IS + ^36 - ^4 - \^6. 
 
 Page 189.-1. VsVlO. 2. Vs^. 3. 4>/6. 4. ^4. 5. 3V3. 
 
 6. 12-f6V3. 7.^^^. 8.^^^^'. 9.^%-^ 
 
 + 6 X — y 4 
 
 ^p 21 + 12 V7 U. -V10-VI5+2V3 + 3V2. 
 
 -^ yg-f Vi0 4-3>S4-^ ,, -^-V6 + 5>S-ViO 
 
 \£. 3^|j 13. ^^^"2 . 
 
 14. -5'J3+Vl5+3Vl0 -3V2. 15. -23 + 4^. 
 ie.35±^ 17. -5 + 2V§. 18.?L±|^. 
 
 o + & * * y 
 
ANSWERS. 17 
 
 Page 191.— 1. 9. 2. "/o. 3. - 1. 4. 11. 5. 2Vj. 6. "/»• 7. 6. 
 8. 2. 9. 7. 10. 1. 11. 3. 12. V26. 13. 8. 14. -6. 15. 3. 16. 7. 
 
 Page 192.— 1. - 5. 2. 16. 3. 8. 4. 3a + c. 
 
 5. - Sx^ - ISy'' ,-f- X +I3y, 6. V - 2x2/. 7. - a + 26 - 2c - 3d. 
 
 8. - 3a + 26 - c + d. 9. (a - 6 + 4c) - (a6 - 2ac + 46c - a26). 
 10. (- a; + 6y - 4z) - {- xy + Sxz - 7yz). 11. (2a;' - 5y^ + 32*) - 
 (2x2 - 2yz - 4a;y). 12. (f - d + 2c - 3e) - (4cd + 3de) + cde. 
 
 Page 193.— 1. x^ + 1. 2. 4<2 + 8< + 1. 3. 4^2 4. 1, 4, _ 4^,2 _ 1^ 
 5. x2 + 2xy + 2/2. 6. m^ - 8m. 7. a; + 5y. 8. 2a;2 + 2y\ 
 
 9. 2a2 - 4a6 + 262. 10. 2a2 - 2a6 - 6^. 11. 64, 81, 4, 1, 1, 1, 5. 
 
 12. aS a«, 4c7, x^, 2/10. 13. a'^, 6-', VsC'S x', x'^. 14. ^' , 30^62, ^ , -^ . 
 
 oa 5 xy 
 
 15. 2a2 4- 262. 15. 2a2 - 2a6 + 562. 17. ^2 + 2a6 - 4ac + 62 
 
 - 46c + 4c2. 18. 4a6 + 562. 19. ^a^ ^ 6ab + 262. 20. - 2a6 + 562. 
 29. 2/2 + 2/ - 2. 30. 2/^ - 62/ + 57. 31. 4x2 + 3x + 2 + 
 
 16x2 _ 25x - 22 
 x' - 2x2 4. 6a. _{_ 5* 
 
 Page 194.— 1. 5xy\2 - 3x). 2. (2x + y){a + 6). 3. 2x(a + 6). 
 4. x'(x + l)(x2 - 6x + 3). 5. x3(x2 + l)(x - 5). 6. (a - 6)2(a + 6). 
 7. (m + n)(x + l)(x ~ 1). 8. (3x2 4. i)(a. _ i)^ 9. (3^ _ 2n)(a2+62). 
 
 10. (m - n)(m - n - 1). 11. (a + y)(h - x). 12. (a2 -f 62)(a - 6). 
 
 13. (2/ + 5)2. 14. (x + 4)2. 15. (06 + 6)2. 16. (a - 6 - c)2. 
 17. (m -f 7)(m - 7). 18. (8 + x)(8 - x). 19. (9x2 4. 5yZ)(gx^ - 5yi), 
 20. (a - 6 + c)(a - 6 - c). 21. (6x + 2/)(- 4x - y). 22. (a + 6 
 + c)(a 4- 6 - c). 23. (x - 4)(x - 1). 24. (x + 4)(x + 1). 
 25. (2/ + 8)(2/ - 2). 26. (y - 8)(y + 2). 27. (x - 2)(x - 5). 
 28. (x + 2)(x 4- 5). 29. (x + 5)(x - 2). 30. (x - 5)(x + 2). 
 31. (a + 9)(a - 2). 32. (6 - 15)(6 + 3). 33. (c + 16)(c - 2). 
 34. (x + 15) (x - 5). 35. (x - 15) (x -f 5). 36. (x - Sy)(x + y). 
 37. x2(l -f 142/)(1 + 2/). 38. (10a + l)(7a + 1). 39. (2x 4- 3)(x + 3). 
 40. (2 + 32/)(l - 22/). 41. (3 - 5m)(2 + 3m). 42. (a 4- 26)(a2 - 
 2a6 4- 462). 43. ^a - 26)(a2 + 2a6 4- 462). 44. (^^ - Sy)i4x^ 4- 6x2/ 
 4- 92/2). 45. (2x + 32/)(4x2 - Qxy + 91/2). 45. ^^2 4. i)(^ 4. i)(a. _ i). 
 
 Pages 195-196.-5. 2. 6. ^1^. 7.7. 8.^. 9.^^. 
 
 10.--^. 11.-^5-. 12.7^2. 13.^,. 14. ^^i. 
 n(a - 6) X - y (x - 2)2 2xy^ y 
 
 15. ^^-qr^ . 10. 5 . 17. ^, ^ 3^ ^ Q . 18. ^2 __ ^, . 
 
 -2m2 ^^ / X ^, a2+26 „ x-2 
 
 l^' —T-t i — i- 20. a(a - x). 21. ^T_ . . 22. ^ . 
 
 m2-|-mn + n2 a + 6 x — 7 
 
18 ANSWERS. 
 
 o« 24y (x — y)» (* — 1)» • 
 
 27 5^-y 28 -° 29 iJ"-^ 
 
 "' (x - y)(x + y) • '*"• (a - 3)(a - 4) ' -«»• 4 ■ 
 
 30.?i±il^. 31.?^±^. 32.^^'. 33.^-. 34, "' 
 
 Pages 196-197.— 1. Vis. 2. 1. 3. 10. 4. - »/«. 5. - "/e.. 
 ^ IV,. 7. -^—. 8. -4-i:. 9. ?-±^. 10. '^ 
 
 11. ^"^^ ; . 12.^-^. 13.-7. 14. »/«. 15.1. 16.3. 
 
 17. 2Vi. 18. Va. 19. - Ve. 20. 1. 21. No root. 22. "/a. 23. 4. 
 24. 5. 25. - "/«. 26. "A, "A- 27. "/i. 19. 28. 2, 5. 29. 2V2, 2Vi. 
 
 30. 6, 5. 31. 1, 1. "" ^^' 
 
 32. 
 
 3 
 
 , c. 
 
 
 5,1. 
 
 
 2 ^^ 
 ^' 2 
 
 J 
 
 
 6. 
 
 - v., - 
 
 v.. 
 
 Pages 197-198.— 1. 5, 1. 2. " "t ^" . 3. 4, 1. 4. 3, - */». 
 
 5. 9, - «/». 6. -- Vj, - Vj. 7. o d: Va» 4- 6^ 
 
 8 (•* 
 
 - 1) ± Vo» 
 
 -6a + l 
 
 
 2 
 
 
 in "" 
 
 • « ± V?« - 
 
 4pr 
 
 AU. 
 
 2p 
 
 * 
 
 
 „ - m ± Vm» - 4j» 
 '• 2 
 
 .. - Vf, 2. 
 
 12. v., v.. 13. 5, v.. 
 
 14. =b Vi. 15. d= VcSTl. 16. «A, 3. 17. d: 6, d= 9. 18. ± 6, d: 4. 
 19. - »/6, 1. 20. 25, 9; - 10, 6. 21. V», Va. 22. Vi, 2. 23. d= 4, ± 3. 
 24. 0, 8; 0, 4. 
 
 Pages 198-200.— 1. 21. 2. 6 hrs.; 50 mi. per hr. 3. 13 ft., 10 fU 
 4. 150 cows. 5. 13 hrs. 6. 50 in., 37 in. 7. 12doz. 8. a = .2, 6 = 1.1, 
 P = 36.18. 9. Mule 7 m. ; donkey 5 m. 10. 10 ft. 11. 400 ft. by 300 ft. 
 12. 15 mi. up, 12 mi. down. 13. $35. 14. 735 lbs. 15. 4Vii gal. 
 16. $416. 
 
 Pages 200-201.-2. 7, 500 lbs. 3. 45V4 lbs. 4. IVm ft. 5. 53V7 in. 
 6. 128"/8»; 83"/8». 7. 3910 lbs. 8. .04 -f in. 9. IVu ft. from heavier 
 end. 10. VVu ft. 
 
 Page 202.— 5. 402.5 ft. 6. 253.7 ft. per sec. 7. About 1247 ft. 
 
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