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3.

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

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7. If

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5. Also of (x + y + x) (x + y - x) (x + x - y), when X = 1, y = 3, % = 5. 6. Prove that a -{y- (x – u)} = x – y + x - u.

= % 1, 6 2, C = 3, prove that a + b + c + 2ab + 2 ac + 2bc = 6 abc = a + b3 + c, 12

', at + 24 + 4 = 14(a + 2c), a + 65 = 11c, a - ab + b = c, (a + b)(a + c)(b + c)

= 10 abc.

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8.

If a =

2, 6

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3, c = 5, and d = 6, find the value of the following expressions : (2a + 3b) (4c – d), (a + b + c - d) (a - 2c + 4 d),

, (26 3d) (a + b 3€ + d), a b + c – , (a + b) (a’b + b'c + c'd), and (a + b +c+d) - a - b - C-d'.

9.

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

=

10.

- X +

Find the value of 11 -x+V2X - V1 – 4*, = 1

when =

11. Replace the radical signs in the following expressions by fractional indices : ♡ (x+y)', Vão + VVx+ Veny, v va Navo ve.

ADDITION.

1.

Add together w* - ax + a2, 2008 + 3a x - 2a',

X and a2 + ax + 3a.

-1

2.

Add together 27+4 a wm-1 + a2mm-, 3x" +2 a 0m-2+a",

and awn-1 + a'wm-2 - 6a".

3.

Add together 2(a + b) - c+d, a + (6 - c) – d,

and a + b – (c- d).

4.

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

– and 3a + b - (3c + d).

5. Add together as +a’b ab? +63, a' (ab+3 ab')-26,

and 2 a' - a b + 2ab +63.

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

and d (b + c - a). 7. Add together a'{b - (c – d)}, ab{b + (a – c)},

and b(c + d a).

8.

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Add together (3a + 2b + c)X, (2a - 36 - 40) X,

and (a + b c) x.

9.

Add together ax by, x- y, and (a – 1) x + (6 + 1) y.

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12.

a

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C

10. Add together 2x + 3 (xy - y'), * - y (2x + 3y),

?

and x(y - 3x) + yo. 11. Add together (a +2b)x - (30–46)y, 2a(x+y)+b(xy)

and 4 ax + 3by. Add together {6-(c-d)},a-b-c-d),a+b-c+d,

and a - (b + c - d). 13. Add together 2a2 + 3a'b - acé + c', ao +2ac2 – 63 + 3c", 3 ab + 4ab? - b'c, and 33 - 3ab? 5 ab 4c.

63

- % 14. Add together 3a4-4a2b+abs +7a2b, 2a4+a’6-6ab3 +64,

and 3ab + 5 a 63 6 a'b*. 15. Add together a'b'e' - ab? + 3 ab'c', abc + 4 a'b' + a'b',

and abc + 2 a'54 - 68. 16. Add together as - (ab + b*), 2 a' (3ab-46%),

and 4 ab + 36.
17. Add together 17a3 + 25 a'b 71 ab' + 2863,

161 a3 - 13a'b + 14 ab - 5163,
19a - 146 a'b + 317 ab – 8063,

?

80bs and 6a3 - 23 a'b - 200 ab + 11263.

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18. Add together 121 a* - 31 a'b + 60 aʼb? + 28ab3 - 4064, *

– 30 a* + 27 a'b - 15a2b2 + 37ab3 + 126, 17 at - 15 a'b 40 a?b- 52 a b3 + 76*,

aʼba at - 3a'b + 43 u'b? - ab3 + 296", and 6a* + a'b - 29 a'b' + 8 ab - 1664.

SUBTRACTION.

1.

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

2. Subtract 2a - 3 (b + c), from a - 2b + 2c.
3. Subtract a (x + y - x) + b (w y + x),
x

@
from (a + b) x + (2a + 3b) y + (a - b)x.

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4.

Subtract aʻx + aby + 2b'x, from 3a (ax + by) - 6*%.

5.

Subtract 24 a'x - 17 a q + 5x3,

x? 5a
from 3a + 25 aʻx 3 a x2 + 10 23.

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6. Subtract 12 (a + b) x – 13 (a - b) y,

·
from 20a (x + 2y) 15b (2x - y).

7.

Subtract 3a:63 + 4 56%, from 3 aš + 9a5b).

8.

Subtract a + 2b + 2 (a - b) – 3 (a − 2b),

from 2a + 3 (b a) – 4 (2b a).

9.

Subtract ax3 + bx2y + C xy' + dy',

from d x3 + cx2y + bx y + ay.

10.

11.

Subtract (a + b - c) x3 + (b + c - d) x’y,

6 from (a + c) x’y - (a - b + c) ys. Subtract x (x? – xy + 3yo) + y (2 x2 + 3xy 2y'),

« +

from x3 + xạy – 3 xy + 2yo. Subtract a - {6 - (c - d)}, from 2a + 3b – (2c-d).

12.

13. Subtract 2a-3 a'b+ ab +63, from 5a + a'b-6ab2 +63.

14.

Subtract at – 4aRb + 6 a’b? 7ab3 + 64,
from 3a' - ab + 7ab2 - 6ab3 + 64.

15.

Subtract 3 a' + 5a'b - ab 3 ab' + 765,
from 3 a5 - 5a'b + 2 a'b3 + 965.

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17.

Subtract a + b + c - d", from a - b - C + d.

?

62 ·

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from 278 a3 - 311 a'b - 21 ab + 146.

MULTIPLICATION.

1. Multiply together a’xy, ax’yo, and a’x’y. 2. Multiply together aaj, x}, and aici. 3. Multiply together a - bx + cx?, and a + bx - cx?.

4. Multiply together a - b + c, a +c – b, and a + b + c.

5. Multiply together x® xy + x*y? xoyjä + aPy4 xy® + yo,

y

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and x + y.

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6. Multiply together 2a3b + 3a?babs + 464,

and a* – 4a2b + a2h2 3 ab3. 7. Multiply together w* – 2x*y + 4 x* y* – 8 xy + 16y',

y

and 22 – 2y. 8. Multiply together quiz 2x + 3, and x2 – x + 1. 9. Multiply together æ; – x} + 2, and x} + 3x} – 1.

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n

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11.

12.

and wm+n + xm+nym+n + ymun, Multiply together a' +b+c ab-ac-bc, and a+b+c. Multiply together a* (b c) + a' (ab - bc),

and a' (ab + bc). 13. Multiply together x – 1, x – 2, and x – 3. 14. Multiply together x2 – 2x + 1, #2 + 2x + 1,

+ and + 2.2" + 1.

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- .

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15. Multiply together x – a, a – b, and x – C.

X 16. Multiply together a + b, a - b, a- ab + b?,

and a2 + ab + 6%.

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