* +

3 xyz.

9. x* + xông? +.

3 a2b + 3 ab2

4 x3y + 4x3%

a2c

4 xy3

4. 0. 7. 4 ab

4.

ac2 b2c bc

4 y3z + 4 xx3

6 x2y2 + 6 x22 + 6 y2x2 - 12 x2yz + 12 xy3z 12. 0.

- 83y + 12 x2y

11. x 2x2y2 + y1.

- 8 xy3 + 2 y

12. a2 + b2 2 c2 + 2 ab 2 ac 2 bc.

1

{a (bc)} d.

6.

8. 0.

− (6 a7b)-(3c5d), 6a+ (7b3c+5 d), -{6a-(76-3c) + 5 d.

7. (423 12 xy) (12xy - 4y3),

8. (a3 63) {a3 - (b3 + c3)} + 9. (ab + (26 C

(၉၆

12 xy)}+ 4 y3.

3 abc), a3 (b3 + c3

3 abc.
d) x2 - (a - b 3 c) xy
f) y2.

ƒ + g
d) x

e

(c = d + e

76

3 abc),

f)y

12. (≈ - x) a2 + (x − y) ab + (y - z) b2.

VI.-PAGE 161.

1. 12 a ab 662, 18 x 9 xy- 35 y2.

2. x3-6 xy + 4 y3, 30 23 + 49 x3y + 9 xy3-4y3.

1. x2-2xy + y2, 9 a2 - 30 ab + 25 b2, 16 c + 8 c2ď2 +ď, 9x12x22 12 x2y2 + 4 y*.

4. (a + c)2 - (b + d)2, (a + b)2 − (c + d)3.

6. x2+4x-5, x2 + 7 x + 10, x2 + 2 x 15, x2- 25.

2. 2 a 5 a3b + 2o a2b2, 2x2 + 3 xy + 2y3.

13. a (p 1) a3 – (p − q − 1) a2 − (p − 1) a + 1.

14. The given expression is—

(a + b + c − d) (a + b − c + d) (a − b + c + d) (a−b — c — d);

20. (ac)2 - 2 (a − c) (b − d) + (b − d)?

IX.-PAGE 177.

1. (x + 3 a) (x - 3 a), (4y2+ 5 x2) (4 y2 – 5 x2), 6 (2a+3b) (2a-36), (2x-3y) (4x2 + 6 xy + 9 y2). 2. x (x − y) (x2 + xy + y2),

(a - b) (a + b) (a2 + b2) (a + ba),

xy (x + y) (x2

xy + y2),

2 xyz (x+2x) (x-2x).

3. (a2 262) (a2 + 2 b2), (x2 + xy + y2) (x2

(a + b)2 (a

b)3 (a + b + c) (a + b

C - d),

c) (a

4. (a + b (a + b a + b

b + c + d),

b + c).

5. 5 (2x+9), 3 (2x+7), (3 a + b − c) (a + b −c). 6. (x2 + xy + y2) { (x − y) (x3 — y3) + 4 x2y2 (x2 — xy — y2)}, (x2 + xy + y2) (x2 xy + y2) (x + y)2 (x 7. (x - 10) (x+7), (x + 1) (x + 10), (a76) (a8b), (x16) (x + 12).

11. 23 + 2x2 + 4x + 8, 3x04 6 x2 + 12 x2

2. a* + 12 a3b + 54 a2b2 +

108 ab3 + 81 b4, 16 a* + 32 a3b + 24 a2b2 + 8 ab3 + b1,

a5 5 a+b+ 10 a3b3 10 a2b3 + 5 aba — b3,

27 a3

108 ab + 144 ab2 64 b3.

5. 1 + 3 x − 5 23 + 3 x3 − x3, (ax + by)3 + 3 (ax + by) cz+ &c.

1

6. 1 + 7 x + 21 x2 + 35 x3 + 35 x2 + 21 x3 + 7 x + x2, (1 + x)1 + 4 (1 + x)3x2 + 6 (1 + x)2x1 + 4 (1 + x)x® + x3, (a + bx) + 4 (a + bx)3 cx2 + &c.

7. a2x2- 8 a7bxy + 28 ab2x2y3 - 56 ab3xy3 +70 a*b*x*y* - 56 ab3x3y + 28 a2b2x2y - 8 ab2x2 + b3y3, 729 x 243 x1y3 + 27 x3y* — y°, 8

2- 3xy3 + 3 x3y3 — y3.

8. 212 2 xoyồ + y1a,

a12-6 a12 + 15 ab* — 20 ab

9. a3 + 3 a3b + 3 ab3 + b3. 11 2 (1 + 3x2)*.

+ 15 a1b3 — 6 a2b1o + b12 10. (a - c)3.

12. 81 x1y (x + y).