9. a44a3x+12 a2x2+16 a x3 + 16x4.

10. x4x3x2 −x + 1.

11.5a24ab3b2.

12. m6+m5x+ m2 x2 + m3 x3 + m2 x4 + m x5 +2.

13. 5 a3 b2 c3-2 a2 b2 c4-3ab2c5-7 b co.

ART. 46.

98.

1. x8+xïy+x® y2 + x5 y3 +x4 y1 + x3 y5 + x2 y®+r y7+

2. 81 a108 a3b+144 a2 b2 +192 a b3+256 b1.

3. x9 — x y + x2 y2 — x6 y3 + x5 y1 — x1 y5 — x3 y¤ — x2 y2+

y9.

4. 1-m+ m2— m3 + m2 — m5+ m2 — m2.

5. m1 - m3 n + m2 n2.

m3 + m2.

m12

1

ma

y5

a x6 y6 1+xy

7. 1 + m2 + m21 + m2 + m2 + m10 +

8. a—axy+ax2 y2—a x3 y3+ax1 y1—a x5 y3 +1 + xy

ART. 47.

1. a2.

2. (m + 1)(a+b).

3. 2(x2 + x + 1) (a+m).

4. (a+b) (x2- xy + y2).

5. 9 (m2 — no) (x4 — x3 y + x2 y2 — x y3 + y1).

9.

50 a x3+26 ax2y+125 ax1+65 a x3 y

17b+3c.

10th and 11th performed.

9.

10.

7 (m5 — m1 y+m3 y2 — m2 y3 +m ya — y5)°

15xy

2 (a+b) (x1 — x3 y + x2 y2 — x y3+y1)°

12.

(m + n) (x4 — x3 y + x2 y2 —x y3+y4)`'

13th and 14th performed.

1. 1, a, a2, b, b2, ab, a2 b, a b2, a2 b2.

2. 1, a, a2, b, ab, a2 b, b2, a b2, a2 b2, c, ac, a3 c, bc, abc, a2bc, b2c, ab2c, a2 b2 c, c2, a c2, a2 c2, bc2, ab c2, a2bc2, b2c2, a b2 c2, a2 b2 c2, c3, a c3, a2 c3, bc3, abc3, a2b c3, b2c3, a b2 c3, a2 b2 c3.

3. 1, 3, 9, x, 3x, 9x, x2, 3x2, 9x2, y, 3y, 9 y, xy, 3xy, 9xy, 2y, 3x2y, 9 x2 y, y2, 3y2, 9 y2, xy2, 3x y2, 9 x y2, x2 y2, 3 x2 y2, 9 x2 y2, y3, 3 y3, 9 y3, x y3, 3 x y3, 9 x y3, x2 y3, 3 x2 y3, 9 x2 y3.

4. 1, 2, 5, 10, 25, 50, m. 2 m, 5m, 10m, 25m, 50m, m2, 2 m2, 5 m2, 10 m2, 25 m2, 50 m2.

5. 1, 2, 3, 6, 5, 10, 15, 30, 25, 50, 75, 150.

6. 1, 2, 4, 3, 6, 12, 5, 10, 20, 15, 30, 60, 13, 26, 52, 39, 78, 156, 65, 130, 269, 195, 399, 780.

7. 1, 2, 4, a, 2 a, 4a, b, 2b, 4b, ab, 2ab, 4ab, a+4, 2(a+4), 4(a+4), a (a+4), 2a (a+4), 4a (a+4), b(a+4) 2b (a+4), 4b(a+4), a b (a + 4), 2 a b (a + 4), 4 ab (a+4).