1.     (i) y – z                      (ii) 

(iii) z²                        (iv) 

(v) x² + y²                (vi) 3mn + 5

(vii) 10 – yz               (viii) ab – (a + b)

2.    (i) 

(ii) 

3.    Sol.

4.   (a) Sol.

(b) Sol.

5.   Sol.

6.   Sol.

7.    (a) Like terms are:

(i) -xy², 2xy²           (ii) -4yx², 20x²y     (iii) 8x² ,-11x²,-6x²

(iv) 7y, y                   (v) -100x, 3x            (vi) -1 lyx, 2xy

(b) Like terms are:

(i) 10pq,-7 pq, 78pq         (ii) 7p, 2405p          (iii) 8q, -100q

(iv) -p²q², 12p²q²             (v) -12,41                  (vi) -5p², 701p²

(vii) 13p²q, qp²

8.    (i) 21b – 32 + 7b – 20b = 21b + 7b – 20b – 32

= 28b – 20b – 32 = 8b – 32

(ii) -z² + 13z² – 5z + 7z³ – 15z = 7z³ + (-z² + 13z²) – (5z + 15z)

= 7z³ +12z² -20z

(iii) p – (p – q) – q – (q – p) = p – p + q – q – q + p

= p – p + p + q – q – q = p – q

(iv) 3a – 2b – ab – (a – b + ab) + 3ab + b – a = 3a – 2b – ab – a + b – ab + 3ab + b – a = 3a – a – a – 2b + b + b – ab – ab + 3ab

= (3a – a – a) – (2b – b – b) – (ab + ab – 3ab)

= a – 0 – (-ab)

= a + ab

(v) 5x²y – 5x² + 3yx² – 3y² + x² – y² + 8xy² – 3y² = 5x²y + 3yx² + 8xy² – 5x² + x² – 3y² – y² – 3y²

= (5x²y + 3x²y) + 8xy² – (5x² – x²) – (3y² + y² + 3y²)

= 8x²y + 8xy² – 4x² – 7 y²

(vi) (3y² + 5y – 4) – (8y – y² – 4) = 3y² + 5y – 4 – 8y + y² + 4

= (3y² + y²) + (5y – 8y) – (4 – 4) = 4y² – 3y – 0 = 4y² – 3y

9.    (i) 3mn, -5mn, 8mn, -4mn = 3mn +(-5mn) + 8mn + (-4mn)

= (3 – 5 + 8 – 4)mn = 2mn

(ii) t – 8tz, 3tz – z, z – t = t – 8tz + 3tz – z + z – t

= t – t – 8tz + 3tz – z + z

= (1 – 1)t + (-8 + 3)tz + (-1 + 1) z = 0 – 5tz + 0 = -5tz

(iii) -7 inn + 5, 12mn + 2, 9mn – 8, -2mn – 3 = -7 mn + 5 + 12mn + 2 + 9mn – 8 + (-2mn) – 3

= -7mn + 12mn + 9mn – 2mn + 5 + 2 – 8 – 3

= (-7 + 12 + 9 – 2)mn + 7 – 11 = 12mn – 4

(iv) a + b – 3, b – a + 3, a – b + 3 = a + b – 3 + b – a + 3 + a – b + 3 = (a – a + a) + (b + b – b) – 3 + 3 + 3 = a + b + 3

(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy = 14x + 10y – 12xy – 13 + 18 – 7x – 10y + 8xy + 4xy

= 14x – 7x + 10y – 10y – 12xy + 8xy + 4xy – 13 + 18

= 7x + Oy + Oxy + 5 = 7x + 5

(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5 = 5m – 7 n + 3n – 4m + 2 + 2m – 3mn – 5

= 5m – 4m + 2m – 7n + 3n – 3mn + 2 – 5

= (5 – 4 + 2)m + (-7 + 3)n – 3mn – 3

= 3m – 4n + 3mn – 3

(vii) 4x2y, -3xy2, -5xy2, 5x2y = 4x2y +(-3xy2) + (-5xy2) + 5x2y

= 4x2y + 5x2y – 3xy2 – 5Xy2

= 9x2y – 8xy2

(viii) 3p2q2 – 4pq + 5, -10p2q2, 15 + 9pq + 7p2q2 = 3p2q2 – 4pq + 5 + (-10p2q2) + 15 + 9pq + 7p2q2

= 3p2q2 – 10p2q2 + 7p2q2 + 4pq + 9pq + 5 + 15

= (3 – 10 + 7) p2q2 + (-4 + 9) pq + 20

= 0p2q2 + 5pq + 20 = 5pq + 20

(ix) ab – 4a, 4b – ab, 4a – ab = ab – 4a + 4b – ab + 4a – ab

= -4a + 4a + 4b – 4b + ab – ab

= 0 + 0 + 0 = 0

(x) x– y2 – 1, y2 – 1 – x2, 1 – x2 – y2 = x– y2 – 1 + y2 – 1 – x+ 1 – x2 – y2

= x2 – x2 – x2 – y+ y2 – y2 – 1 – 1 + 1

= (1 – 1 – 1)x+ (-1 + 1 – 1)y2 – 1 – 1 + 1

= -x2 -y2 -1

10.  (i) y2 – (-5y2) = y2 + 5y2 = 6y2

(ii) -12xy – (6xy) = – 12xy – 6xy = -18xy

(iii) (a + b) – (a – b) = a + b – a + b = a – a + b + b = 2b

(iv) b (5 – a) – a (b – 5) = 5b – ab – ab + 5a = 5b – 2ab + 5a = 5a + 5b – 2ab

(v) 4m2 – 3mn + 8 – (-m+ 5mn) = 4m2 – 3mn + 8 + m2 – 5mn

= 4m+ m2 – 3mn – 5mn + 8

= 5m2 – 8mn+8

(vi) 5x – 10 – (-x+ 10x – 5) = 5x – 10 + x2 – 10x + 5

= x+ 5x – 10x – 10 + 5 = x2 – 5x – 5

(vii) 3ab – 2a2 – 2b2 – (5a2 – 7 ab + 5b2) = 3ab – 2a2 – 2b2 – 5a+ 7 ab – 5b2

= 3ab + 7 ab – 2a2 – 5a2 – 2b2 – 5b2

= 10ab – 7a2 – 7b2

= -7a2 – 7b+ 10ab

(viii) 5p+ 3q2 -pq – (4pq – 5q2 – 3p2) = 5p2 + 3q2 -pq – 4pq + 5p+ 3p2

= 5p+ 3p+ 3q+ 5q2 – pq – 4pq

= 8p2 – 8q2 – 5pq

11.  (a) Let p should be added.

Then according to question,

x2 + xy + y+ p = 2x+ 3xy          ⇒        p = 2x+ 3xy – (x+ xy + y2)

⇒ p = 2x+ 3xy – x2 – xy – y2         ⇒       p – 2x2 – x2 – y2 + 3xy xy

⇒ p = x2 – y2 + 2xy

Hence, x2 – y+ 2xy should be added.

(b) Let q should be subtracted.

Then according to question,

⇒ 2a + 819 + 10 – q= -3a + 7b + 16       ⇒           -q = -3a + 7b + 16 – (2a + 8b + 10)

⇒ -q = -3a + 7b + 16 – 2a – 8b – 10         ⇒          -q = -3a – 2a + 7b – 8b + 16 – 10

⇒ -q= -5a – b + 6                      ⇒                     q = -(-5a – b + 6)

⇒ q = 5a + b – 6

12.  Let q should be subtracted.

Then according to question,

3x2 – 4y+ 5xy + 20 – q = -x2 – y+ 6xy + 20

⇒ q = 3x2 – 4y+ 5xy + 20 – (-x2 – y+ 6xy + 20)

⇒ q = 3x2 – 4y2 + 5xy + 20 + x+ y2 – 6xy – 20

⇒ q = 3x2 + x2 – 4y2 + y + 5xy + 20 + x2 + y2 – 6xy – 20

⇒ q = 4x2 – 3y2 – xy + 0

Hence, 4x2 – 3y2 – xy should be subtracted.

13.  (a) According to question,

(3x – y + 11) + (-y – 11) – (3x – y – 11) = 3x – y + 11 – y – 11 – 3x + y + 11

= 3x – 3x – y – y + y + 11 – 11 + 11

= (3 – 3)x – (1 + 1 – 1)y + 11 + 11 – 11

= Ox – y + 11 = – y + 11

(b) According to question,

[(4 + 3x) + (5 – 4x + 2x2)] – [(3x2 – 5x) + (-x2 + 2x + 5)]

= [4 + 3x + 5 – 4x + 2x2] – [3x2 – 5x – x2 + 2x + 5]

= [2x2 + 3x – 4x + 5 + 4] – [3x2 – x2 + 2x – 5x + 5]

= [2x2 – x + 9] – [2x2 – 3x + 5]

= 2x2 – x + 9 – 2x2 + 3x – 5

= 2x2 – 2x2 – x + 3x + 9 – 5

= 2x + 4.

14.  (i) m – 2 = 2 – 2 = 0                     [Putting m = 2]

(ii) 3m – 5 = 3 × 2 – 5 = 6 – 5 = 1       [Putting m = 2]

(iii) 9 – 5m = 9 – 5 × 2 = 9 – 10 = -1    [Putting m = 2]

(iv) 3m2 – 2m – 7 = 3(2)– 2(2) – 7           [Putting m = 2]

= 3 × 4 – 2 × 2 – 7 = 12 – 4 – 7

= 12 – 11 = 1

15.  (i) 4p + 7 = 4(-2) + 7          [Putting p = -2]

= -8 + 7 = -1

(ii) -3p2 + 4p + 7 = -3(-2)2 + 4 (-2) + 7    [Putting p = -2 ]

= -3 × 4 – 8 + 7 = -12 – 8 + 7

= -20 + 7 = -13

(iii) -2p– 3p2 + 4p + 7 = -3(-2)+ 4(-2) + 7                       [Putting p = -2 ]

= -2 × (-8) – 3 × 4 – 8 + 7 = 16 – 12 – 8 + 7

= -20 + 23 = 3

16.  (i) 2x – 7 = 2(-1) – 7                [Putting x = -1]

= -2 – 7 = -9

(ii) -x + 2 = -(-1) + 2                [Putting x = -1]

= 1 + 2 = 3

(iii) x+ 2x + 1 = (-1)+ 2(-1) + 1      [Putting x = -1]

= 1 – 2 + 1 = 2 – 2 = 0

(iv) 2x2 – x – 2 = 2(-1)2 – (-1) – 2          [Putting x = -1]

= 2 × 1 + 1 – 2 = 2 + 1 – 2

= 3 – 2

= 1.

17.  (i) a2 + b2 = (2)2 + (2)2               [Putting a = 2, b = -2 ]

= 4 + 4 = 8

(ii) a2 + ab + b2 = (2)2 + (2) (-2) + (-2)2                    [Putting a = 2, b = -2 ]

= 4 – 4 + 4 = 4

(iii) a2 – b2 = (2)2 + (2)2 = 4 – 4 = 0             [Putting a = 2, b = -2 ]

18.  (i) 2a + 2b = 2 (0) + 2 (-1)                  [Putting a =0, b = -1]

= 0 – 2 = -2

(ii) 2a2 + b2 + 1 = 2(0)2 + (-1)2 + 1     [Putting a =0, b = -1]

= 2 × 0 + 1 + 1 = 0 + 2 = 2

(iii) 2a2b + 2ab2 + ab = 2(0)2 (-1) + 2(0)(-1)2 + (0)(-1)      [Putting a =0, b = -1]

= 0 + 0 + 0 = 0

(iv) a2 + ab + 2 = (0)2 + (0)(-1) + 2          [Putting a =0, b = -1]

= 0 + 0 + 2 = 2

19.  (i) x + 7 + 4 (x – 5) = x + 7 + 4x – 20 = x + 4x + 7 – 20              [Putting x = 2]

= 5x – 13 = 5 × 2 – 13

= 10 – 13 = -3

(ii) 3(x + 2) + 5x – 7 = 3x + 6 + 5x – 7 = 3x + 5x + 6 – 7          [Putting x = -1]

= 8x – 1 = 8 × 2 – 1

= 16 – 1 = 15

(iii) 6x + 5 (x – 2) = 6x + 5x -10 = 11x – 10         [Putting x = -1]

= 11 × 2 – 10

= 22 – 10 = 12

(iv) 4 (2x – 1) + 3x + 11 = 8x – 4 + 3x + 11 = 8x + 3x – 4 + 11       [Putting x = -1]

= 11x + 7 = 11 × 2 + 7

= 22 + 7 = 29

20.  (i) 3x – 5 – x + 9 = 3x – x – 5 + 9 = 2x + 4          [Putting x = 3]

= 2 × 3 + 4

= 6 + 4 = 10

(ii) 2 – 8x + 4x + 4 = -8x + 4x + 2 + 4 = -4x + 6      [Putting x = 3]

= -4 × 3 + 6

= -12 + 6 = -12

(iii) 3a + 5 – 8a + 1 = 3a – 8a + 5 + 1 = -5a + 6

= -5(-1) + 6                             [Putting a = -1]

= 5 + 6 = 11

(iv) 10 – 3b – 4 – 5b = -3b – 5b + 10 – 4 = -8b + 6

= -8(-2) + 6                              [Putting b = -2]

= 16 + 6 = 22

(v) 2a – 2b – 4 – 5 + a = 2a + a – 2b – 4 – 5

= 3a – 2b – 9 = 3(-1)-2(-2)-9             [Putting a = -1, b = -2]

= -3 + 4 – 9 = -8

21.  (i) z3 – 3(z – 10) = (10)– 3(10 – 10)

= 1000 – 3 × 0 = 1000 – 0 = 1000

(ii) p2 – 2p – 100 = (-10)2 – 2(-10) – 100

= 100 + 20 – 100 = 20

22.  Given: 2x2 + x – a = 5

⇒ 2(0)+ 0 – a = 5                                [Putting x = 0]

⇒ 0 + 0 – a = 5                        ⇒         a = -5

Hence, the value of a is -5.

23.  Given: 2(a+ ab) + 3 – ab

⇒ 2a+ 2ab + 3 – ab              ⇒           2a2 + 2ab – ab + 3

⇒ 2a+ ab + 3

⇒ 2(5)2 + (5)(-3) + 3                    [Putting a = 5, b = -3]

⇒ 2 × 25 – 15 + 3

⇒ 50 – 15 + 3

⇒ 38

24.  Sol.

(i) 5n + 1

Putting n = 5,     5 × 5 + 1 = 25 + 1 = 26

Putting n = 10,    5 × 10 + 1 = 50 + 1 = 51

(ii) Putting 3n + 1     n = 100,  5 × 100 + 1 = 500 + 1 = 501

Putting n = 5,      3 × 5 + 1 = 15 + 1 = 16

Putting n = 10,     3 × 10 + 1 = 30 + 1 = 31

(iii) Putting 5n + 2      n = 100, 3 × 100 + 1 = 300 + 1 = 301

Putting n = 5,      5 × 5 + 2 = 25 + 2 = 27

Putting n = 10,    5 × 10 + 2 = 50 + 2 = 52

Putting n = 100,  5 × 100 + 2 = 500 + 2 =   502

25.  (i) 2n – 1

Putting n = 100, 2 × 100 – 1 = 200 – 1 = 199

(ii) 3n + 2

Putting n = 5, 3 × 5 + 2 = 15 + 2 = 17

Putting n = 10, 3 × 10 + 2 = 30 + 2 = 32

Putting n = 100, 3 × 100 + 2 = 300 + 2 = 302

(iii) 4n + 1

Putting n = 5, 4 × 5 + 1 = 20 + 1 = 21

Putting n = 10, 4 × 10 + 1 = 40 + 1 = 41

Putting n = 100, 4 × 100 + 1 = 400 + 1 = 401

(iv) 7n + 20

Putting n = 5, 7 × 5 + 20 = 25 + 20 = 55

Putting n = 10, 7 × 10 + 20 = 70 + 20 = 90

Putting n = 100, 7 × 100 + 20 = 700 + 20 = 720

(v) n2 + 1

Putting n = 5, 5 × 5 + 1 = 25 + 1 = 26

Putting n = 10, 10 × 10 + 1 = 100 + 1 = 101

Putting n = 100, 100 × 100 + 1 = 10000 + 1 = 10001

Now complete table is,