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**Exercise 12.3 **

**Question 1: If m = 2, find the value of: **

**(i) m - 2 (ii) 3m - 5 (iii) 9 - 5m(iv) 3m**

**Answer 1: **

**(i)** m - 2 = 2 - 2 [Putting m = 2]

= 0

**(ii)** 3m - 5 = 3 x 2 - 5 [Putting m = 2]

= 6 - 5 = 1

**(iii)** 9 - 5m = 9 - 5 x 2 [Putting m = 2]

= 9 - 10 = - 1

**(iv) **3m^{2} - 2m - 7

= 3(2)^{2} - 2 (2) - 7 [Putting m = 2]**=3 x 4 - 2 x 2 - 7 = 12-4-7 = 12- 11 = 1(v)** [Putting m = 2]

= 5 - 4 = 1

**Question 2: **

**If p = -2, find the value of:**

**(i) 4p + 7(ii) - 3p ^{2} + 4p + 7 (iii) -2p^{3} - 3p^{2} +4/7 + 7**

**Answer 2: **

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

= -8 + 7 = -1

**(ii) **-3p^{2}+4p + 7

= -3 (-2)^{2}+ 4 (-2) + 7 [Putting p = - 2]

= - 3 x 4 - 8 + 7

= - 12 - 8 + 7

= -20 + 7 = -13

**(iii)** - 2p^{3} - 3p^{2} +4p + 7

= - 2 (-2)^{3} - 3(-2)^{2 }+ 4 (-2) + 7 [Putting p = - 2]

= -2 x(-8)-3 x4 -8 + 7

= 16-12-8 + 7

= -20 + 23 = 3

**Question 3: **

**Find the value of the following expressions, when x = -1: **

**(i) 2x - 7(ii) -x + 2(iii) x**

**Answer 3: **

**(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^{2} + 2 x + 1 = (-1)^{2} + 2 (-1) + 1 [Putting x= - 1]

= 1 - 2 + 1

= 2 - 2 = 0

**(iv)** 2x^{2}- x - 2 = 2 (-1)^{2} - (-1) - 2 [Putting x= - 1]

= 2x1 + 1-2

= 2 + 1 - 2

= 3 - 2 = 1

**Question 4: **

**If a = 2,b = -2, find the value of: **

**(i) a ^{2} + b^{2 }**

(ii) a^{2}+ab + b^{2}

(iii) a^{2} - b^{2}

**Answer 4: **

**(i) **a^{2} + b^{2} ( 2)^{2} + (- 2)^{2} [Putting a = 2. b = - 2 ]

= 4 + 4 = 8

**(ii)** a^{2}+ab + b^{2 }

= (2) + ( 2) (- 2) +(-2)^{2 }[Putting a = 2. b = - 2 ]

= 4 - 4 + 4 = 4

(iii) a^{2} - b^{2} = (2)^{2} - (-2)^{2} [Putting a = 2,b = - 2]

= 4 - 4 = 0

**Question 5: **

**When a = 0, b = -1, find the value of the given expressions: **

**(i) 2a + 2b(ii) 2a ^{2}+b^{2}+1 (iii) 2a^{2}b + 2ab^{2} +ab(iv) a^{2}+ab+2**

**Answer 5: **

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

= 0 - 2 = -2

**(ii) **2a^{2} + b^{2} + 1 = 2 (0)^{2} + (-1)^{2} + 1 [Putting a - 0,b = - 1]

= 2 x 0 + 1+ 1 = 0 + 2 = 2

**(iii) **2a^{2}b + 2ab^{2} + ab = 2(0)^{2} (-1) + 2 (0 )(-1)^{2} + (0 )(-1) [Putting a - 0,b = - 1]

= 0 + 0 + 0 = 0

**(iv) **a^{2} +ab + 2 - (0)^{2} + (0) (-1) + 2 [Putting a - 0,b = - 1]

= 0 + 0 + 2 = 2

**Question 6: **

**Simplify the expressions and find the value if x is equal to 2: **

**(i) x + 7 + 4 (x- 5)(ii) 3 (x + 2) + 5x - 7(iii) 6x + 5 (x - 2)(iv) 4 (2x - 1) + 3x + 11**

**Answer 6: **

**(i)** x + 7 + 4(x- 5) = x + 7 + 4x - 20 = x + 4 x + 7 - 20

= 5 x - 13 = 5 x 2 - 13 [Putting x = 2]

= 10-13 = -3

**(ii)** 3 (x+ 2) + 5x - 7 = 3x + 6 + 5x -7 = 3x + 5x + 6 - 7

= 8x - 1 = 8 x 2-1 [Putting x = -1]

= 16 - 1 = 15

**(iii)** 6x + 5 (x - 2) = 6x + 5x -10 = 11x - 10

= 11 x 2 - 10 [Putting x = -1]

= 22 - 10 = 12

**(iv) **4(2x - 1) + 3x + 11 = 8x - 4 + 3x +11 = 8x + 3a - 4 + 11

= 11a + 7 = 11 x 2 + 7 [Putting x = - 1]

= 22+7 = 29

**Question 7: **

Simplify these expressions and find their values if x = 3,a = -1, b = - 2 :

(i) 3x - 5 - x + 9

(ii) 2 - 8x + 4x + 4

(iii) 3a + 5 - 8a + 1

(iv) 10 - 3b - 4 - 5b

(v) 2a - 2b - 4 - 5 + a

**Answer 7:**

**(i) **3a - 5 - x + 9 = 3x - x - 5 + 9 = 2x + 4

= 2x3+4 [Putting a = 3]

= 6 + 4 = 10

**(ii) **2 - 8x + 4x + 4 = - 8x + 4x + 2 + 4 = -4x + 6

= - 4 x 3 + 6 [Putting a = 3]

= -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

**Question 8: **

**(i) If z = 10, find the value of z ^{3} - 3 (z - 10).(ii) If p = - 10, find the value of p^{2} - 2p - 100**

**Answer 8: **

**(i) **z^{3} -3(z-10) = (10)^{3}-3(10 - 10) [Putting z = 10]

= 1000 - 3 x 0 = 1000- 0

= 1000

**(ii) **p^{2} - 2p - 100 = (-10)^{2} - 2 (-10) - 100 (Putting p = - 10]

= 100+ 20 - 100 = 20

**Question 9: **

**What should be the value of a if the value of 2x ^{2} + x - a equals to 5, when x = 0 ? **

**Answer 9: **

**Given: **2x^{2} + x - a = 5

â‡’ 2 (0)^{2} + 0 - a = 5 [Putting x = 0]

â‡’ 0 + 0 - a = 5

â‡’ a = -5

Hence, the value of a is -5.

**Question 10: **

**Simplify the expression and find its value when a = 5 and b = - 3: 2 (a ^{2} + ab) + 3 - ab**

**Answer 10: **

Given : 2 (a^{2} + ab) + 3 - ab

â‡’ 2a^{2} + 2ab + 3 - ab

â‡’ 2a^{2} + 2ab - ab + 3

â‡’ 2a^{2} + ab + 3

â‡’ 2 (5)^{2} + (5) (-3) + 3 [Putting a = 5 , b = -3]

â‡’ 2 x 25 - 15 + 3

â‡’ 50 - 15 + 3

â‡’ 38

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