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3.

when x = 2.

Also of (2a + y) (2x + 3y), when a = 2, y = 3.

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Also of (x + y + x) (x + y − ≈) (x + x − y), when

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6.

Prove that a{y − (≈ − u)} = x − y + z − u.

7. İf

α = 1, b = 2, c = 3, prove that

a2 + b2 + c2+2ab+2ac+2bc6abc a3 + b3 + c3,

aa + ba + c1 = 14(a + 2c),

ας + 65 = 11c,

a2 - ab+b2 = c,

=

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8. If a = 2, b = 3, c = 5, and d = 6, find the value of the following expressions:

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

(2b - 3d) (a + b − 3c + d), a2 – b2 + c2 — ď2,

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(a3 + b3) (a3b + b3c + c3d), and (a + b + c + d)3 − a3 − b3 — c3 – ď3.

9. Find the value of x3-3x2+3x-1, when x 3.

10.

=

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when = 12. x

11. Replace the radical signs in the following expressions by fractional indices :

√ (x + y)3, √ a3x + √ b3x2 + √ c1æ3‚ √√√a, Va√ √c.

ADDITION.

1. Add together x2- ax + a2, 2x2+3ax - 2 a3,
and x2 + ax + 3a2.

2. Add together xTM+4axTM-1+a2xm-2, 3x+2α2xm−2+am, and am-1+ a2xm-2-6a".

3.

4.

5.

Add together 2 (a + b) − c + d, a + (b −c) - d,

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Add together a + 2c+d, 2a (bc) d,

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Add together a3 + a2b− ab2 + b3, a3 − (a2b+3ab3) — 2b3,

and 2a3a2b+2ab2 + b3.

6. Add together a (b + c − d), b(a + d −c), c(a + d−b),

and d (b + c − a).

7. Add together a {b (cd)}, ab{b + (a − c)},

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8. Add together (3a + 2b + c)x, (2a-3b-4c) x, and (a + b −c) x.

9. Add together ax-by, x-y, and (a− 1) x + (b + 1)y.

10. —

11.

12.

Add together 2x2 + 3 (xy − y3), xo − y (2x + 3y), and x(y − 3x) + y2.

Add together (a+2b)x−(3a-4b)y, 2a(x+y)+b(x−y) and 4ax + 3by.

Add together a {b−(c–d)},a-b-(c–d), a+b−c+d,

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13. Add together 2 a3+3a2b- ac2 + c3, a3 +2 ac2 — b3 + 3 c3, 3a2b+4ab2 - b3c, and b3 – зab2 - 5a2b - 4c3.

14.

15.

Add together sa1—4a3b+ab3+7a2b3,2a1+a3b-6ab3+ba, and 3ab5ab3 - 6a2b2.

Add together a2b3c2 — a1b2 + 3 ab3c3, abc1 + 4a2b1 + a1b3, and ab3c+2a2b1 — bo.

16. Add together a2 − (ab + b2), 2a3 — (3ab−4b2), and 4ab3bo.

17.

Add together 17a3+25ab71ab2 + 28b3,

161 a3-13a2b+14ab25163,

19a3 - 146ab + 317 ab2 - 80b3,

and 6a3-23 a2b - 200 ab2 + 112b3.

18. a1 Add together 121 a 31 ab + 60 a2b2 + 28 a b3 - 40 b1,

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Subtract ab+ cd, from 2a+b-c+ 3d.

1.

2.

Subtract 2a 3 (b + c), from a − 2b + 2c.

3. Subtract a (x + y − x) + b (x − y + x),

from (a + b) x + (2a + 3b) y + (a − b)x.

4. Subtract ax+aby+2bx, from 3a (ax+by) - b'x.

5. Subtract 24a x 17a x2+5x3,

6.

from 3a+25a2x-3a x2+10x3.

Subtract 12 (a + b) x 13 (a - b) y,
from 20a (x

+ 2 y) − 15b (2x − y).

7.

Subtract 3ab + 4a3

– 5b3, from 3a +9aba.

8. Subtract a + 2 b + 2 (a - b) — 3 (a - 2b),

from 2a + 3 (b− a) — 4 (2b − a).

9. Subtract ax3 + bx2y + cxy2 + dy3,

10.

11.

12.

from da3 + ca2y + bx y2 + ay3.

Subtract (a + b − c) x3 + (b + c − d) x2y,

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Subtract x (x2- xy + 3y3) + y (2x2 + 3xÿ − 2y3),
from æ3 + x2y − 3xy2 + 2y3.

Subtract a - {b
{b (cd)}, from 2a+3b - (2c-d).

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13. Subtract 2a3-3a2b+ab+b3, from 5a3 + a3b − 6ab2+b3.

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Subtract a2+b2 + c2 - d, from a b2 - c2 + d2.

18.

Subtract 256 a3-317a2b+19ab2 - 36b3,

from 278a3311ab21 ab2 + 14b3.

MULTIPLICATION.

1. Multiply together a2xy3, ax2y3, and a3x3y. 2. Multiply together ala, ax, and axl.

3. Multiply together a bx + ca2, and a + bx − cx2.

4. Multiply together a − b + c, a + c − b, and a + b + c.

·

4

5. Multiply together x − xy + x1y2 — x3y3 + x2y1 — xy3+yo,

and x + y.

6. Multiply together 2a3b+3a2b2 — ab3 + 4b1,

and a 4a3b+ a2b2 - 3ab3.

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7. Multiply together x1- 2x3y + 4x2 y2 − 8xy3 + 16y1, and x2-2y3.

8. Multiply together x2 - 2x + 3, and ∞2 − ∞ + 1.

9. Multiply together aa +2, and x + 3æ3 − 1.

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10. Multiply together am+- xm+n ym+n + ym+n,

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11. Multiply together a2+b2+c2-ab-ac-bc, and a+b+c.

12. Multiply together a1 (b − c) + a3 (ab − bc),

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and a (ab+bc).

13. Multiply together x 1, x2, and ≈ – 3.

14.

Multiply together a2 - 2x + 1, x2 + 2x + 1,
and +22 + 1.

15. Multiply together xa, ab, and x – c.

16. Multiply together a + b, a − b, a2 - ab + b2,

and a2 + ab + b2.

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