NCERT Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.3

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:
= m = 2
= (3 × 2) - 5
= 6 - 5
= 1

(iii) 9 - 5m
Answer:
= m = 2
= 9 - (5 × 2)
= 9 - 10
= -1

(iv) 3m² - 2m – 7
Answer:
= m = 2
= (3 × 2²) - (2 × 2) – 7
= (3 × 4) - (4) - 7
= 12 - 4 -7
= 12 - 11
= 1

(v) (5m/2) - 4
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:
= p = -2
= (4 × (-2)) + 7
= -8 + 7
= -1

(ii) -3p² + 4p + 7
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:
= 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:
= x = -1
= (2 × -1) - 7
= -2 - 7
= -9

(ii) - x + 2
Answer:
= x = -1
= - (-1) + 2
= 1 + 2
= 3

(iii) x² + 2x + 1
Answer:
= x = -1
= (-1)² + (2 × -1) + 1
= 1 - 2 + 1
= 2 - 2
= 0

(iv) 2x² - x - 2
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:
a = 2, b = -2
= (2)² + (-2)²
= 4 + 4
= 8

(ii) a² + ab + b²
Answer:
a = 2, b = -2
= 2² + (2 × -2) + (-2)²
= 4 + (-4) + (4)
= 4 - 4 + 4
= 4

(iii) a² - b²
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:
a = 0, b = -1
= (2 × 0) + (2 × -1)
= 0 - 2
= -2

(ii) 2a² + b² + 1
Answer:
a = 0, b = -1
= (2 × 0²) + (-1)² + 1
= 0 + 1 + 1
= 2

(iii) 2a²b + 2ab² + ab
Answer:
a = 0, b = -1
= (2 × 0² × -1) + (2 × 0 × (-1)²) + (0 × -1)
= 0 + 0 +0
= 0

(iv) a² + ab + 2
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:
= 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:
= x = 2
= 3x + 6 + 5x - 7
= 8x - 1
= (8 × 2) - 1
= 16 - 1
= 15

(iii) 6x + 5 (x - 2)
Answer:
= x = 2
= 6x + 5x - 10
= 11x - 10
= (11 × 2) - 10
= 22 - 10
= 12

(iv) 4(2x - 1) + 3x + 11
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:
= x = 3
= 3x - x - 5 + 9
= 2x + 4
= (2 × 3) + 4
= 6 + 4
= 10

(ii) 2 - 8x + 4x + 4
Answer:
= x = 3
= 2 + 4 - 8x + 4x
= 6 - 4x
= 6 - (4 × 3)
= 6 - 12
= -6

(iii) 3a + 5 - 8a + 1
Answer:
= a = -1
= 3a - 8a + 5 + 1
= -5a + 6
= - (5 × (-1)) + 6
= - (-5) + 6
= 5 + 6
= 11

(iv) 10 - 3b - 4 - 5b
Answer:
= b = -2
= 10 - 4 - 3b - 5b
= 6 - 8b
= 6 - (8 × (-2))
= 6 - (-16)
= 6 + 16
= 22

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