18

2

(18 )

2.1 (1 )

2.2 (2 )

2.3 (2 )

2.4 (4 )

2.5 (4 )

2.6 (5 )

1.

2.

19

2.1

1.

2.

2.1

1. x y

2. 2.1

3.

-5 x -5 x -5

-5x0 x 1 x

1

2.2

1.

2.

2.2 2.2 2.2

1.

1, 2 3

-3 5

21

0.75

2x 3x

19

20

-5a2

2a2

7pq 0.2pq

-2x2y 3yx

2

–

2.

–

3x4 + 2x

4 = (3 + 2)x

4

= 5 x4

2.2

3.

2.2

4. 2.2

2.3

1.

2.

1.

1) 5a -2a

2) 2x 3y

3)

(1) x2 + 3x

2y

(2) 3x2y – 2xy

(3) xy + yz – zx

(4) x2y

2 + 7z

2y

2

(5) x2 + y

2 + z

2

20

21

2.

x

y

2x + 2y

3.

2.4

1.

2.

1. – 4 – 5

2.

1) -5 5

2) -5 (-1)(5)

3) -x x

4) -x (-1)(x)

5) -(x+2 ) x+2

6) -(x +2) (-1)(x+2)

-(x + 2) = (-1)(x + 2)

= (-1)(x) + (-1)(2) ( )

= (-x) + (-2)

y

x

y

x

21

22

x + 2 (-x) + (-2)

-(x + 2) x + 2

x + 2 (-x) + (-2)

-x x

-2 2

x – 2 x – 2

x – 2 x + (-2) x + (-2)

- [x+ (-2)] = (- x) + 2

-x x 2 -2

3. x2 – 7xy – 6

x2 – 7xy – 6 = -(x

2 – 7xy – 6)

-(x2 – 7xy – 6) = -[x

2 + (-7xy) + (-6)]

-(x2 – 7xy – 6) = -x

2 + 7xy + 6

4.

1) 6x2 – (2x

2 – x) = 6x

2 – 2x

2 + x

= 4x2 – x

2) (4x3 – 5x

2) – (3x

3 + x

2 – 1) = 4x

3 – 5x

2 – 3x

3 – x

2 + 1

= x3 – 6x

2 + 1

5.

6.

22

23

+ =

7. 2.4 3 5) 6)

3) 5) 2) 6)

8.

9. “ ”

2.5

2.5 2.5

1.

2.

4

3. “ ”

1)

(2x3 + 4x) + (5x

2 – 2x

3) = 5x

2 + 4x

-2x4 + (2x

4 – 5) = -5

2)

(1)

(-2) (3x2 – 5) = -6x

2 + 10

23

24

(2)

4x(3x2 – x + 1) = 12x

3 – 4x

2 + 4x

4. “ ”

2.5

5. 2.5

2.6

2.6

1.

2.

5

43 = 54

53

7

2 6 = 72

76

x

3xx 2

= x

3x x

x 2

3x

xx 23

= 3xx

3xx 23

3. ( )

4.

=

24

25

5. “ ”

6. 2.6

2.1

1.

1) -1, 0 2) 1, 0

3) 1, 1 4) -0.17, 0

5)38

, 4 6) -5, 1

7) -31

, 1 8) 2, 3

9) -1, 3 10) 9, 9

11) -51

, 5 12) 1, 4

13) -1, 2 14) -1, 4

15)6

13, 7 16) -4 , 6

17)37

, 2 18) -81

, 3

2. 2x, 2-1x

2 5x

3

3. -3x2y

2, -3x

3y -3xy

3

38

8xy2, - 45

16 xy2 51xy

2

-12x2y 3

2 x2y

34 xy -xy

25

26

2.2

1.

1) 2)

3) 4)

5) 6)

7) 8)

9) 10)

2.

1) -5x 2) 18y

3) 6x + 6y 4) 23

5) 5x2

6) 3yz

7) 2x2y + xy

2 8) 4y

5

9) -7x4y – 7xy

410) -tx

3

3.

1) 13x 2) -2y

3) 6x – 6y 4) -47

5) x2

6) 7yz

7) 2x2y – xy

2 8) 0

9) -7x4y + 7xy

410) -7tx

3

4.

1) 3x 2) -23y

3) 6x 4) -18y

5) 6u 6) 3w2

7) 12r2s 8) 0

9) 2x2– 3y

2 + 6z

3 10) 9st + 4s

2t2

5.

1) 0 2) 4y

3) 5z 4) 13y2

5) x2

6) 0

7) -17s3

8) 0

9) 6xy 10) 8xy2

11) -yz 12) -29s2 t

26

27

48

1) 0 2) 0

3) 1 4) 1

5) 2 6) 1

7) 2 8) 2

2.3

1.

1) 2x – 10

2) 3z2

3) 3x3 – 2x

2

4) 2x – xy + 4

5) 3x2y + y

2 + 6

2.

1) 1

2) 2

3) 3

4) 2

5) 3

3.

1) 8x + 3

2) -3y2 + 6y

3) -13z3 – 10z

2

4) -5z3 – 4z

2 – 5z

5) x2 – 7x – 2

4.

1) 3 + 2x

2) 5 – 3x + x2

3) -5 + 6x – 2x2

5) 4 + 7x – x3

6) 1 – x + 8x2 + 4x

3

27

28

2.4

1.

1) -7x + 15 2) x – 14

3) -9x + 5y + 4 4) 7z2 + 3z – 10

5) 6x2 + 12 x – 1 6) -6s + 2st

7) 10xy – 11st 8) x2 – 2x – 1

9) - r + 9s – 9t 10) 3x + 17y – z – 13

11) y2 – 3y + 2 12) 4r – 2x – y

2.

1) 2x – 2y 2) 11x + 4y + 17

3) 3x + y – 8 4) 18z2 + 10z + 1

5) -7x2 –3x + 8 6) 2x

2 + 5x – 11

7) -7x2 + x + 8 8) 2x

2 – 2x – 9

9) 3x – 4 10) -6r + 6s + 6t

11) 21x – 9 12) -3x2 – 16x – 17

2.4

1.

1) 2x – 7 2) -20x + 11

3) 0 4) -7x2 + 14x + 3

5) -2x2 –2x – 10 6) 9x

2 – 18x – 10

2.

1) -7xy + 3x + y – 23xy – 3x + 3y

2) 4z2 + 16z – 4 4z

2 – 2z – 6

3) -2x – 21 2x2 – 10x + 21

4) 6r + 16s – 10t -6r + 10s – 6t

5) 8x2 – 6x – 5 2x

2 + 18x – 3

6) 23

x2 –

35

x + 12 21

x2 +

31

x – 8

28

29

3.

1) 9x2 – 8x – 20 2) -x

2 – 12x – 6

3) -5x2 + 10x + 4 4) -15x

2 + 6x +18

5) -13x2 + 7x + 10 6) 3x

2 + 13x – 2

2.5

1.

1) 6x2

2) xy

3) 27xy 4) 4x3

5) 2xy2

6) 0

7) 52x2y 8) -99x

2y

3

9) -12x4y 10) -60x

3y

3

11) -28y3z

2 12) -56y

4z

4

2.

1) 30x + 12 2) 2x + 3

3) x2 – x 4) 56x

2 – 63x

5) 20x2+ 18x 6) -4x

2 + 24x

7) -5x3 – 40x 8) 6x

2 – 8x –14

9) 9x3 + 18x

2 – 27x 10) 7x

4 – 10x

3

11) -6x4 + 3x

2 – 18x 12) -48x

4 + 40x

3 – 88x

2

1.

2.

29

30

2.6

1) -2x 2) 5x

3) 3x

4) 2

y2

5) 4y 6) 23

xy

7) -4x2

8) 3xy

9) 45

x2

10) -x2y

11) 6y2

12) 21

x2y

2.6

1.

1) 2x – 4 2) -2x + 5

3) 2x2 + 1 4) x

2 – 4

5) 3x2 – 5x 6) 3x + 8

7) 2x – 3 8) 3x – 7

9) 1 – 4x 10) -x2 – 6x + 1

2.

1) 45

– 4

3x 2) 2x

2 + 4

3) 5

4x–

51

4) 5 – 4x2

5) -3 – 7x2

6) 8x – 3

7) -3x + 4 8) -1 – 3x

9) 6x2 – 5x + 3 10) x

2 –

43x

– 2

3.

1) 4x2 – 4x 2) 3x

2 – 7x

3) 10x – 4x3

4) -18x3 –24x

2

5) -7x3 + 28x

2 6) -15x

3 + 5x

2 –30x

30

3131

32

x

x

2.1

1. AB AB

[x ]

2. CD 3 AB CD

[3x ]

3. x

[x2 ]

4. x

[x 3

]

5. x 4

[4 x2

]

A B

x

xx

x

x

32

33

6. x y

[xy ]

7. 6 4

[4xy ]

8. x y z

[xyz ]

y

x

x

y

yx

z

33

34

2.2

1.

( ) ( ) ( ) ( )

2 3 (2 2) + (2 3) = 10 2 3 = 6

3 5 (2 3) + (2 5) = 16 3 5 = 15

4 5 (2 4) + (2 5) = 18 4 5 = 20

7

x

10

y

(2 7) + (2 10) = 34

2x + 2y

7 10 = 70

x y = xy

2.

x y

2x + 2y xy

.

.

.

.

.

.

.

.

.

.

.

.

34

35

2.2

1. 5 + 3 [ 8 ]

2. 5.4a + 6.7a [ 12.1a ]

3. 7x + (-13)x [ -6x ]

4. -5x2 + 5x

2 [ 0 ]

5. x21 + x

31

[ x ]

6. 11.5ab + (-6.3ab) [ 5.2ab ]

7. [2xy + xy] + (-xy) [2xy ]

8. xy xy 21 +

41 xy [ xy ]

9. 3

m 3

+ 4m3 +

32m 3

[5m3]

10. -4m3 +

32m

3m 33

[-3m3]

11. xy + (-2xy) + (-3xy) [-4xy ]

12. [-12pqr + 7pqr] + (-5pqr) [ -10pqr ]

13. -12pqr + [ 7pqr + (-5pqr)] [ -10pqr ]

14. [-3x3 + 15x

3 ]+[ 3x

3 + (-12x

3)] [ 3x

3 ]

15. [-3x3 + 3x

3 ]+ [15x

3 + (-12x

3)] [ 3x

3 ]

5

6

_

7

4

_

35

36

2.2

1. 11 – 23 [ -12 ]

2. 2.8x – (-3x) [ 5.8x ]

3. -5x – 9x [ -14x ]

4. 2x2 – (- 4 x

2) – 2 x

2[ 4x

2 ]

5. 3x2y – 4 x

2y – 5 x

2y [ -6x

2y ]

6. -4m – 3m – (-7m) [0]

7. 7pq – (11pq – 9pq) [ 5pq ]

8. (7pq – 11pq) – 9pq [ -13pq ]

9. 24xy – 6xy – 14 xy [ 4xy ]

10. 3xyz – (7xyz – xyz) [-3xy ]

11. (3xyz –7xyz) – xyz [-5xy ]

12. (2ab – ab + ab) – (2ab – 2ab) [ 2ab ]

13. (2ab – ab)+ (ab –2ab – 2ab) [ -2ab ]

14. -5x2y – (-6x

2y) – 5x

2y – 6 x

2y [ -10x

2y ]

15. [-5x2y – (-6x

2y)] – [5x

2y + (-6 x

2y)] [ 2x

2y ]

36

37

2.5

1. 6 6 30

2. 6 2 50

3. 6 3 10

1. 3

5 1

2.

x

1 x

y x

1)

x2

x

xy

x

x

x x

1 y

37

38

2)

……… [x ]

……… [x + 3 ]

[x(x + 3)]

……… [x2 + 3x ]

3)

2x

(

)

……… [x - 2 ]

……… [x ]

………

[x(x - 2)]

..……

[x2 - 2x ]

4)

x

x 11 1

x

x

y

x – 2 1 1

x

x

38

39

……… [x ]

……… [x + y ]

[x(x + y)]

……… [x2 + xy ]

3. 2 – 3

39

40

2.5

1. 4 4

5 5 6 6 7 7

2. 1

1

2

………… …………[4 (4 – 2)] + 4 [4 (5 – 2)] + 4

12 16

(2 4) + 2(4 – 2) …………(2 5) + 2(5 – 2)

12 16

…………

40

41

3

3. n n

1

1 1 = (2 n) + 2 (n – 2)

= 2n + 2n – 4

= 4n – 4

= 4(n – 1)

2 1 = 4 (n – 2) + 4

= [(4 n) – (4 2)] + 4

= 4n – 8 + 4

= 4n – 4

= 4(n – 1)

3 1 = 4 (n – 1)

= 4(n – 1)

4.

4n – 4 4(n – 1)

5.

20 20

1

4 (5 – 1) ………… …………4 (4 – 1)

12 16

41

42

n2 – 4(n – 1) = 20

2 – (4 19)

= 400 – 76

= 324

324

42

4343

44

2.6

1.

1) 6a – 4a – 5a [-3a]

2) 5x2y + 6x

2y [11x

2y]

3) 7pq + 11pq – 9pq [9pq]

4) 24xy – 6xy – 8xy [10xy]

5) -3x2y

3 + 7x

2y

3 – 15x

2y

3[-11x

2y

3]

2.

1) 3x – 2 + x – 9 [4x – 11 1]

2) 2a + 5 –

4a – 3 [ + 2 1]

3) -5x3 – 2x

2 + 5x

3 – x [-2x

2 – x 2]

4) a3 + a

2 + 3 + a

3 + 2a – a

2[2a

3 + 2a + 3 3]

5) -18xy – 6x2y + 15xy [-6x

2y – 3xy 3]

3.

1) (2x + 5) + (3x – 7) [5x – 2]

2) (4x2 – 6) + (x

2 – 5x + 4) [5x

2 – 5x – 2]

3) (3x2 – 7) – (x + 5) [3x

2 – x – 12]

4) (4x2 – 5x) – (-3x

2 – 5) [7x

2 – 5x + 5]

5) (-5x2 + 8x – 1) – (-4x

2 – 2x + 3) [-x

2 + 10 x – 4]

4)

1) (-9x3)(2x

2) [-18x

5]

2) (7x3)(-x

2y) [-7x

5y]

3) (-10a2b

3)(-2ab) [20a

3b

4]

4) 8xy (-2xy) [-4]

5) (-15a2b

3) (-3ab

2) [5ab]

6) (-24mn2) (6mn) [-4n]

5.

1) (-5)(2x2 – 3) [-10x

2 + 15]

2) 7m (-2m2 + m + 1) [-14m

3 + 7m

2 + 7m]

3) (-2mn)(3m2 – n) [-6m

3n + 2mn

2]

4) (xy)(-1 + 2x – 3y) [-xy + 2x2y – 3xy

2]

5) x2(4x

2 – 3x – 5) [4x

4 – 3x

3 – 5x

2]

a

2

_

44

45

6.

1) (x2 – 2x) x [x – 2]

2) (10a3 + 4a

2 – a) (2a) [5a

2 + 2a – ]

3) (-9x2 – 12x + 4) (-3) [3x

2 + 4x – ]

4) (25x3 – 10x

2 – 15x) (5x) [5x

2 – 2x – 3]

5) (-14x2y – 7xy

2 + 21xy) (-7xy) [2x + y – 3]

7. a b [a – b ]

8. 2x, y x

[3x + y ]

9. ( x y

)

[x2 + 2xy ]

10. x y z

[xy + 2yz + 2xz ]

y

x y

y

y

x

z

yx

2

1_

3

4_

45