Answers to Elementary algebra

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IN MEMORIAM
FLORIAN CAJORl

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Answers

TO

-EMENTARY AlGEEEA

DY

FLORIAN CAJORI

AND

LETITIA ODELL

Beat pork

THE MACMILLAN COMPANY

1916

A II rights reserved

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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 0

^^•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.^%-^

0 + 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.

14 DAY USE

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General Library

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THE UNIVERSITY OF CALIFORNIA LIBRARY

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