## Chapter 12 Algebraic Expressions Exercise 12.3

**Question 1: If m = 2, find the value of:(i) m - 2 Answer:**

= m = 2

= 2 - 2

= 0

**(ii) 3m - 5**

Answer:

Answer:

= m = 2

= (3 × 2) - 5

= 6 - 5

= 1

**(iii) 9 - 5m**

Answer:

Answer:

= m = 2

= 9 - (5 × 2)

= 9 - 10

= -1

**(iv) 3m² - 2m – 7**

Answer:

Answer:

= m = 2

= (3 × 2²) - (2 × 2) – 7

= (3 × 4) - (4) - 7

= 12 - 4 -7

= 12 - 11

= 1

**(v) (5m/2) - 4**

Answer:

Answer:

= m = 2

= ((5 × 2)/2) - 4

= (10/2) - 4

= 5 - 4

= 1

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

(i) 4p + 7

Answer:

(i) 4p + 7

Answer:

= p = -2

= (4 × (-2)) + 7

= -8 + 7

= -1

**(ii) -3p² + 4p + 7**

Answer:

Answer:

= p = -2

= (-3 × (-2)²) + (4 × (-2)) + 7

= (-3 × 4) + (-8) + 7

= -12 - 8 + 7

= -20 + 7

= -13

**(iii) - 2p³ - 3p² + 4p + 7**

Answer:

Answer:

= p = -2

= (-2 × (-2)³) - (3 × (-2)²) + (4 × (-2)) + 7

= (-2 × -8) - (3 × 4) + (-8) + 7

= 16 - 12 - 8 + 7

= 23 - 20

= 3

**Question 3: Find the value of the following expressions, when x = -1:**

(i) 2x - 7

Answer:

(i) 2x - 7

Answer:

= x = -1

= (2 × -1) - 7

= -2 - 7

= -9

**(ii) - x + 2**

Answer:

Answer:

= x = -1

= - (-1) + 2

= 1 + 2

= 3

**(iii) x² + 2x + 1**

Answer:

Answer:

= x = -1

= (-1)² + (2 × -1) + 1

= 1 - 2 + 1

= 2 - 2

= 0

**(iv) 2x² - x - 2**

Answer:

Answer:

= x = -1

= (2 × (-1)²) - (-1) – 2

= (2 × 1) + 1 - 2

= 2 + 1 - 2

= 3 - 2

= 1

**Question 4: If a = 2, b = -2, find the value of:**

(i) a² + b²

Answer:

(i) a² + b²

Answer:

a = 2, b = -2

= (2)² + (-2)²

= 4 + 4

= 8

**(ii) a² + ab + b²**

Answer:

Answer:

a = 2, b = -2

= 2² + (2 × -2) + (-2)²

= 4 + (-4) + (4)

= 4 - 4 + 4

= 4

**(iii) a² - b²**

Answer:

Answer:

a = 2, b = -2

= 22 - (-2)2

= 4 - (4)

= 4 - 4

= 0

**Question 5: When a = 0, b = -1, find the value of the given expressions:**

(i) 2a + 2b

Answer:

(i) 2a + 2b

Answer:

a = 0, b = -1

= (2 × 0) + (2 × -1)

= 0 - 2

= -2

**(ii) 2a² + b² + 1**

Answer:

Answer:

a = 0, b = -1

= (2 × 0²) + (-1)² + 1

= 0 + 1 + 1

= 2

**(iii) 2a²b + 2ab² + ab**

Answer:

Answer:

a = 0, b = -1

= (2 × 0² × -1) + (2 × 0 × (-1)²) + (0 × -1)

= 0 + 0 +0

= 0

**(iv) a² + ab + 2**

Answer:

Answer:

a = 0, b = -1

= (0²) + (0 × (-1)) + 2

= 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)

Answer:

(i) x + 7 + 4 (x - 5)

Answer:

= x = 2

= x + 7 + 4x - 20

= 5x + 7 - 20

= (5 × 2) + 7 - 20

= 10 + 7 - 20

= 17 - 20

= -3

**(ii) 3 (x + 2) + 5x – 7**

Answer:

Answer:

= x = 2

= 3x + 6 + 5x - 7

= 8x - 1

= (8 × 2) - 1

= 16 - 1

= 15

**(iii) 6x + 5 (x - 2)**

Answer:

Answer:

= x = 2

= 6x + 5x - 10

= 11x - 10

= (11 × 2) - 10

= 22 - 10

= 12

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

Answer:

Answer:

= x = 2

= 8x - 4 + 3x + 11

= 11x + 7

= (11 × 2) + 7

= 22 + 7

= 29

**Question 7: Simplify these expressions and find their values if x = 3, a = -1, b = -2.**

(i) 3x - 5 - x + 9

Answer:

(i) 3x - 5 - x + 9

Answer:

= x = 3

= 3x - x - 5 + 9

= 2x + 4

= (2 × 3) + 4

= 6 + 4

= 10

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

Answer:

Answer:

= x = 3

= 2 + 4 - 8x + 4x

= 6 - 4x

= 6 - (4 × 3)

= 6 - 12

= -6

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

Answer:

Answer:

= a = -1

= 3a - 8a + 5 + 1

= -5a + 6

= - (5 × (-1)) + 6

= - (-5) + 6

= 5 + 6

= 11

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

Answer:

Answer:

= b = -2

= 10 - 4 - 3b - 5b

= 6 - 8b

= 6 - (8 × (-2))

= 6 - (-16)

= 6 + 16

= 22

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

Answer:

Answer:

= a = -1, b = -2

= 2a + a - 2b - 4 - 5

= 3a - 2b - 9

= (3 × (-1)) - (2 × (-2)) - 9

= -3 - (-4) - 9

= -3 + 4 - 9

= -12 + 4

= -8

**Question 8: (i) If z = 10, find the value of z³ - 3(z - 10).**

Answer:

Answer:

= z = 10

= z³ - 3z + 30

= (10)³ - (3 × 10) + 30

= 1000 - 30 + 30

= 1000

**(ii) If p = - 10, find the value of p² - 2p – 100**

Answer:

Answer:

= p = -10

= p² - 2p - 100

= (-10)² - (2 × (-10)) - 100

= 100 + 20 - 100

= 20

**Question 9: What should be the value of a if the value of 2x² + x - a equals to 5, when x = 0?**

Answer:

Answer:

= x = 0

= 2x² + x - a = 5

= a = 2x² + x - 5

a = (2 × 0²) + 0 - 5

a = 0 + 0 - 5

a = -5

**Question 10: Simplify the expression and find its value when a = 5 and b = -3.**

2(a² + ab) + 3 - ab

Answer:

2(a² + ab) + 3 - ab

Answer:

= a = 5 and b = -3

= 2a² + 2ab + 3 - ab

= 2a² + ab + 3

= (2 × 5²) + (5 × (-3)) + 3

= (2 × 25) + (-15) + 3

= 50 - 15 + 3

= 53 - 15

= 38

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