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If a = 2b, d=26, then result = 2(26 ) (c - 20)

= 2(6)(-c)

- 2bc.

8.

.

3x + 6y - 72
2x – 7y + 52

x + y + 3

6x - -2.
2y - 3y - (x - y)} = 2y - 3y + 3x – 3y= 3.x – 4y
2x - 3{* - (y - x)} = 2x – 3x + 3y - 3x = - 4x + 3y

7x 79

= 7(x - y). 9. A power in Algebra is the product of two or more equal factors.

The root of a quantity is the factor which, multiplied by itself a certain number of times, will produce the given quantity—e.g., the square root of 4 is 2, because the square of 2, or 2 x 2, = 4 10.

7x – 11+ 3Vxyz

16+ 8 xys - y - 6x - 10Vxyz + 5y

- 143' + 4% 10x – 15

Jayz - 10y + 42 5.x – 16+ 2Vxyz – 11Y - 52 5x+ 1 - 3Vxyz +

+ y + 92. 11.

6a - 8b
ба 76
зба? – 48ab

42ab + 5662
za – 40)362- 9006 + 560°(122 – 140

48ab
- 42ab + 5662
- 42ab + 5662

9.0 - 20

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12.

(a - b)x -(6-cy
(a+b)x+ (6 + cly
2bx – 2by = -26(x + y),

- 25(x + y)
which divided by *+y=

(x+y)

= - 2b.

=

13. 3a - [a+b-{a+b+c-(a+b+c+d)}]

= 32 - [a+b - a+b+c-a-b-c-d}]
= 3a - [a+b-{-d}]
= 3a - [a+b+d]= 3a - a-b-d

= 29 -6-d.
2a - 6-d
2a +b+d
4a2 2ab - zad
+ 2ab - 62 - bd

zad - bd - 09
402 62 - 2bd - d2.

14.

xc? + 4xy + 4y2
2 - 4xy + 4y2
24 +4*y + 4x2y2
- 4x3y – 16x2y2 – 16x13

4x4y2 + 16X22 + 1674
** - 8x* ya + 16y4
43 – 2x”y – 4xy2 + 8y3).** - 8xy2 + 16y4 *+ 2y

44 – 2x*y – 4**y+ Sxys!

2x%y - 47°2 - 8xy + 163* 2x*y - 4722 - 8x18 + 16y4

15. {2(x + y) + 3(x - y)} {2(x+y) – 3(x - y)}

= 4(x + y)2 - 9(x - y)
= 4(x2 + 2xy + y2) - 9(x2 - 2xy + yo) )
= 4x2 + 8xy + 4y3 – 9.x2 + 18xy - 9y3
= 26xy - 5.x2 - 5y2

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17. (x + 2) (x + 3) = x2 + 5x + 6, and x(x + 1) = x2 + x.

x2 + 5x + 6

+ x
** + 528 + 6x2

*8 + 5x2 + 6x

** + 6x3 +1172 + 6x, Adding one to this product, we have ** + 6x® + 11x? +6x + 1. ** + 3x + 1)** + 6x8 + 11x2 +6x + 16x2 + 3x + 1

13* +32° + x2

3x3 + 10x? + 6x
3.73 + 9.x2 + 3.1

*2 + 3x + 1
*2 + 3x + 1

4a2

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- 3ax3

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00

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23

18. 3x2 + ax

x2 - ax + }a
3.44 + ax3 - 4a x?

ax + 4ax

sa x2 + fax – 20+
3.x+ - 2ax3 - 34a-x2 + 4%a3x - 2a4.
32 +y – 7)2y + 16y2+159+42(12 – 3y + 26

yt +

- 323 + 23y2 + 159
- 3у3 – 3у2 + 2 у

26y2 - 6y + 42
26y2 + 26y – 182

- 32y + 224. 19. (a + b) (6+c)-(c+d) (d+a) (6+c) (6-d)

: {ab + ac +62 + bc} - {cd +ac+d2 + ad} - {82 bd + bc - ud? = ab + ac + b2 + bc - cd - ac d2 ad - 52 + bd bc+cd = ab - ad + bd - d2. If b=2, d=1,

result = 2a - ļa+1-1

=a+* = *(2a + 1).
24 + 3x3 +7*2 + 15x + 10
x2 – 3x + 2
@ + 3x5 + 734 + 15x3 + 10x?
- 3.45 – 2x4 – 2 143 – 45x2 – 30x

2x4 + 6x3 + 140x2 + 30x + 20
26

- 2 1/2

+ 20
*2 + 3x + 2).** – 21x2 + 20. (** – 348 + 732 – 15x + 10

3.25 - 204
3x5 – 9X4 - 6x3

734 + 6x3 - 21x2
7** + 21x3 + 14x2

- 1533 – 35x2
- 15.23 – 45.42 - 30x

20.

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25

.

x® +

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10x2 + 30x + 20 10x9 + 30x + 20

.

21. 5a-b(m + n) x - 6ac(m + n)2

= - 300*bcm + n);
and – 30a4bcm + n)3 = - 15abcm + n)
- 30a+bcm + n)

= 2a.
- 15abc(m + n)

S

22. (x2 - y2 – 22)8 = {(x2 - y2) – 22}3 = (x2 - y2)3 – 3(x2 - y2)232

+3(x2 - y24 - 30 = (36 – 3x4y2 + 3x2y4 – 46) – 3(<4 – 2x2y2 + y4)z2 + 3x274

- 3y2,4 – 20 = 36 – 3x4y2 + 3x2y4 – 38 – 3x432 + 6x2y2z2 – 3y4z2 + 3x274

- 3y224 – 26.

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23. (am - a*)3 = (am) – 3(am)?an + 3am(an)2 – (a”)3

= a3m – 3a2m2n + 3ama2n – a3n = 28m – 3a2m+n + 3am+2n - 23n.

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24. (2m – 3n)4 = 34m – 4.33m2n + 6x2mx2n – 4xM331 + x4n

4x3m+n + 6x2m+n) – 40m+31 + x4n.

= x4m

25. (3x + 2y)3 – (2x + 3y)3 =(2723 + 54.xoy+ 36xy2 + 8y3) -(8x3 + 36x”y + 54xy2 + 27y3) = 1983 + 18x2y – 18xy2 – 1998.

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x - y)19x3 + 18x2y – 18xy2 – 1993/19.x2 + 37xy + 1972

( (
Isco – 191°y

37x*y – 18xy2
37x4y - 37xy2

19xy2 – 1933
19xy2 - 1993

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