7/30/2019 COMALGE

1/2

COMALGE PRACTICE EXERCISES 1

I. Know the structure of the real number system ( rational, irrational, integers, natural numbers, decimals)

Know also the properties of real numbers.

II. Perform the indicated operations

1. Add 22 y5xyx2 and 22 y6xy5x7

2. Subtract 2a + 2b 4c from the sum of 4a 7b + 12c and 5b 3c

3. 9x ( 2y 3x) { y ( 2y - x) } [ 2y + 2 ( 4x - 3y) ]4. }a]3)3a(5a2[4a{a5a2 223

5. a. 465 )35( b. 374343 )yx2()yx4( c. 2870 )y5)(yx5(

d. (25)(2-7)(2-2) e. (3s5t-4)-6 f. (-5m-1n4)3(n-3m-2)-7

6. a.2

6a9

2bc

4

0c

3b

2a3 b. 2

v2

u33

u2

w284

w7

3v

2u3

c.6b3

32b3b

da

)da(.

n2p21p

p1n22n

)yx(

)yx(

7. a.43

3 6

2 232

3 2b.

2 3 7

3 3 0

43a b c

2a b cc.

1 3 5

1 2 3

9 t y

(4 ty )d.

2a 1

a 1 n

9

(3 )

e. 35

1419

1010

1010

f. 3243

4312

zyx6

zyx4

g.

22

22

213

wvu

wvu

8. a. 3xy( 2x 3y ) ( x + 5y ) b. )xy4(yx2)yx3x2(xy3 22

9. a. )3x3x2)(1x4x4( 22 b. )y3xy4x)(yxy3x2( 2222

10. )1x)(10xx2( nn2

11. a. Divide 4x4x5x6 23 by 2x + 3 b. Divide 3x2x4 3 by 2x - 1

12. a. Divide 4x4x5x4243 by x + 2 b. Divide 16a4n - 64a10n by 2a3n

13. a. Divide 1xxx259 by 1xx

2 b. Divide 3x8x4x3 24 by 2x6x3 2

14. a. Divide x3 + y3 by x 2y b. Divide 4x2- 6xy- 3y2 by 2x + 3y

c. Divide 3z3

-11z2

x - 18zx2

- 6x3

by z - 5xIII. Use special product formulas to find the following.

1. ( 7x + 3y ) ( 2x 4y) 12. ( 6m + 5n) ( 6m + 5n )

2. ( 2mn 3r) ( 5mn + 2r ) 13. )2t5( 3 )2t5( 3

3.2)y3x5( 14. 3nn )yx(

4. 232 )y2x3( 15. 2)z2yx5(

5. 243 )z3yx5( 16. 2)c2b6a(

6. 3)yx4( 17. 2)w3z2yx2(

7. 32 )c2xy( 18. ]z4)y2x3[( ]z4)y2x3[(

8. 32 )xx3( 19. ]3)xx2[( 2 ]3)xx2[( 2

9. ( 4x - 3y) ( 4x + 3y) 20. [ 2( x + y) 5] [ 3 ( x + y) + 4 ]

10. )b7a5( 43 )b7a5( 43 21. )]1x()xx2[( 32 )]1x()xx2[( 32

11. )(4c

3

ab)(

4c

3

ab22. )]yx()b2a[( 232 )]yx()b2a[( 232

IV. Factor the following completely.

1. x10x4x2 23 16. 20abba 22

2. 232232 zxy4yzx12zxy6 17. 6x11x102

3. 3y (2x + 5) 4x (2x + 5) 18. 4224 q6qp13p6

4. 22 )y3x(xz6)y3x(x3 19. 456 x9x24x16

5. 22 z16x52 20. 22 y25xy10x

6. 684 zyx4 21. baaba2

7. 643 xd9yx 22. d6c3cd4c22

8. 42 r4)z3x2(81 23. 224 x1x2x

9. 22 )n3m4(4a64 24. yz18xz24xy3x4 2

10. 33 ba27 25. bcacbab2a 22

7/30/2019 COMALGE

2/2

11. 63 b8a 26.2233 yxy2xyx

12. 912 yx8 27. 3322 dc8d3cd5c2

13. 33 a)b3x(64 28. )7x4()3x(8)7x4)(3x(2 22

14. acb4a9 223 29. 4)yx(23)yx(62

15. 94 y81yx625 30. 2222 ba9)y9xy12x4(25

V. Reduce the ff fractions to lowest terms.

1.7

52

xy30

yx362.

3a8a4

3a7a62

2

3.x3

27x3

4.3b4bb12

1b432

2

VI. Perform the indicated operations

1.324

23

yx8

xy27

xy24

yx402.

y412

9y6y

9y

15yy 2

2

2

3.

dc

bc

dc

bdbc

dc

dcc

22

22

22

23

4.22

2

22

22

22

33

y9x

y3xy

yxy3x9

y3xy2x

yxy4x3

yx27

5.x

3x

2x

1x6.

x53

yx2

3x5

y2x3

7.22 x4x2

3

3x12

28.

3x

1x

9x

6x6

3x

x2

9.a3

2

3a

110.

8x10x3

3x2

12xx6

3x

6xx2

1x2222

11.1x

1x2x

)x1(x

1x2

2

12.2x

4x

1x

1

2x

3

13.c1

c

3c3

2c

5c3

2c14.

9x6x

x

3x

2x

9x6x

2x3

3x

x322

15.2x3

x

2x5x12

1x56x

216.

x

1

1x

x

1x

2

17.

x2

1

4

1

x

1x

4

2

1

2

3

18.

1x2

x1211x2

3

2x

5

19.

x

11

1xx

1x

xx

2

2

20.

y

x21

11

x

1

21.

q2p

qp2

q2p

1

qp

2

VII. Simplify the ff expressions

1.1

11

)yx(

yx2.

1221

2112

yx2yx

x6yxy3.

223

232

yya

yaa

4. 122 )yx( 5. 2

4

)3x(8

)3x(46.

11vu

vu7.

11

22

xy

yxxy