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[blocks in formation]

9. Side of the base 31.072+ feet; altitude 124.288+ feet. 10. Radius 2 feet; length 7 feet.

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ART. 107.

1. m2-2 mx+x2.

2. a3 c+3a2bc +3 a b2 c+b3 c.

3. a2m+2abm+b2 m +2 a cm+2bcm+c2 m+a2 n + 2 abn+b2n+2acn+2bcn+c2n.

4. a3 x2+2 a3 x y + a3 y2.

5. 4c2+12cd +9 d2.

6.

a2+2ab+b2

c3+3c2d+3cd2 + d3°

SECTION XXXIX.

ART. 113.

1. a7+7 a b + 21 a5 b2 +35 a1 b3 + 35 a3 b1 +21 a2 b5 + 7 a b + b2.

2. x10+10x9 y +45 x8 y2+120 x y3 +210 x ya + 252 x3 y5 +210 x1 y® + 120 x3 y1 + 45 x2 y3 + 10 x y3 + y1o ̧

3. m5-5 m2 n + 10 m3 n2 - 10 m2 n3 +5 m n1 — n5.

4. 61111b10 c +55 b9 c2+165 b8 c3 +330 b7 c4 +462 b6 c5

+462 b5 c6 +330 b4 c7 + 165 b3 c8

5. x13 — 13 x12 y + 78 x11 y2
x13

+ 55 b2 c9 +11 b c1o + c11. 286 x1o y3 +715 xo y1 — x10

1287 x8 y5+ 1716 x7 yo — 1716 x6 y7 +

286 x3 y1o — 78 x2 y11 + 13 x y12 — y13.

6. Performed.

1287 x5 y3 — 715 xa yo +

7. x5 +10 x4 y + 40 x3 y2 + 80 x2 y3 + 80 x y1 +32 y3.
8. 216 a3 +540 a2 x + 450 a x2 + 125 x3.

9. Performed.

10. 32 a5 +240 a1 x + 720 a3 x2 + 1080 a2 x3 + 810 a x2 + 243 x5.

11. 64 x3-144 x2 y + 108 x y2-27 y3+48 a x2-72 a x y +27 ay2+12 a2 x — 9 a2 y + a3.

12. a3 +3 a2 b + 3 a b2 + b3 +3 a2c+6 a b c +3 b2 c + 3 a2 d + 6 a b d + 3 b2 d + 3 a c2 + 6 a c d + 3 a d2 +3 b c2+ 6 b c d + 3 b d2 + c3 +3 c2 d + 3 c d2 + d3.

[ocr errors]

13. a12a5b-6 a3 c +60 a1 b2-60 a4 b c + 15 at c2 +160 a3 b3-240 a3 b2c+120 a3 b c2 20 a3 c3 +240 a2 b4 -480 a2 b3 c + 360 a2 b2c2-120 a2bc3+15 a2c4+ 192 a b5 -480 a b c +480 a b3 c2-240 a b2 c3 +60 a b c1 — 6 a c3 + 192 b5 c + 240 b4 c2 160 b3 c3 + 60 b2 c4 12 b c5

64 66 ta

[ocr errors]

14. a5 +5 ab + 10 a3 b2 + 10 a2 b3 + 5 a b1 + b5

c5

10 a4 c

-40 a3 bc-60 a2 b2 c· ·40 a b3 c. -15 a1 d. -60 a3 b d -90 a2 b2 d

[ocr errors]

[ocr errors]

-60 a b3 d-15 b4 d + 40 a3 c2 + 120 a2bc2 + 120 a b2 c2 + 40 b3 c2 + 120 a3 c d + 360 a2 b c d + 360 a b2 c d +120 b3 c d + 90 a3 d2 + 270 a2 b d2 + 270 a b2 d2

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[ocr errors]

-

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- 270 b2 ď3 +80 a c2 + 480 a c3 d + 1080 a c2 d2 + 1080 a c d3 +405 a d1+80 b c1 + 480 b c3 d + 1080 b c2 d2 + 1080 b c d3

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In this article the answers are indefinite, and, therefore, they are not given.

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