9. a1+4a3 x + 12 a2 x2 + 16 a x3 + 16 x1.

10. x4x3x2 −x+1.

+

11.5a2+4ab3b2.

12. m6+m5 x + m2 x2 + m3 x3 + m2 x4 + m x5 +21.

13. 5 a3 b2 c3 2 a2 b2 c4 -3 a b2 c5.

ART. 46.

7 b c6.

1. x8+x7y+x6 y2 + x5 y3 +x1 y1+x3 y5 + x2 y¤ + x y2+

2. 81 a1+108 a3 b + 144 a2 b2 + 192 a b3 +256 64.

3. x9 — x y + x7 y2 — x6 y3 + x5 y1 — x4 y5 + x3 y6 ——— x2 y7+

x y8 — y9.

4. 1-m+m3 — m3 + m2 — m5 + m3 — m2.

5. m1— m3 n + m2 n2.

· m5

- m n3 + n1.

6. m3 — m2 + m2 — m3 + m1 — m3 + m2 — m +1.

7. 1+ m2 + m2 + m2 + m2 + m1o +1=m22

8. α

a x y + a x2 y2 — a x3 y3 + a x1 y1 — a x5 y5 +

ART. 47.

1. a2.

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

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

4. (a+b) (x2- x y + y2).

5. 9 (m2 — n2) (x4 — x3 y + x2 y2 — x y3 + y1). 6. 3 m (x3 — y3) (m2 +n3).

7. 5 (m2 — 1) (x4 — x3 + x2 — x + 1).

9.

5.

b -C

12 a4+25 a3 b

6.

b2+2 ac

a2x—b2x+a3y-by b+c

7.

4 a2 c2 4 62 c2

8.

m2+2mn+n3°

50 a x3 +26 a x2 y + 125 a x2 + 65 a x3 y

17b+3c.

10th and 11th performed.

9.

10.

7 (m3 —m1 y+m3 y2 — m2 y3 +m y1— y5)°

15xy

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

1. 1, a, a2, b, b2, ab, a2b, a b2, a2 b2.

2. 1, a, a2, b, ab, a2 b, b2, a b2, a2b2, c, ac, a2c, bc, abc, a2bc, b2c, a b2 c, a2 b2 c, c2, a c2, a2 c2, b c2, a b c2, a2 b c2, b2 c2, a b2 c2, a2 b2 c2, c3, a c3, a2 c3, bc3, ab c3, a2bc3, b2 c3, a b2 c3, a2 b2 c3.

3. 1, 3, 9, x, 3x, 9x, x2, 3x2, 9x2, y, 3y, 9 y, xy, 3xy, 9xy, x2y, 3x2y, 9 x2y, y2, 3 y2, 9 y2, x y2, 3 x 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, 5 m, 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, 260, 195, 390, 780.

7. 1, 2, 4, a, 2a, 4 a, b, 2b, 4b, ab, 2ab, 4 ab, a +4, 2(a+4), 4(a+4), a (a+4), 2a (a+4), 4a (a+4), b(a+4), 2b (a4), 4b(a+4), a b (a+4), 2 ab (a+4), 4 ab (a+4).