ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.3
Question 1.
If m = 2, find the value of:
(i) 3m – 5
(ii) 9 – 5m
(iii) 3m2 – 2m – 1
(iv) \(\frac { 5 }{ 2 }\) m – 4
Solution:
(i) 3m – 5 = 3 × 2 – 5 = 6 – 5 = 1
(ii) 9 – 5m = 9 – 5 × 2 = 9 – 10 = -1
(iii) 3m2 – 2m – 7
= 3(2)2 – 2 × 2 – 7
= 12 – 4 – 7
= 12 – 11
= 1
(iv) \(\frac { 5 }{ 2 }\) m – 4 = \(\frac { 5 }{ 2 }\) × 2 – 4 = 5 – 4 = 1
Question 2.
If p = -2, find the value of:
(1) 4p + 7
(ii) -3p2 + 4p + 7
(iii) -2p3 – 3p2 + 4p + 7
Solution:
p = -2
(i) 4p + 7
= 4 × (-2) + 7
= -8 + 7
= -1
(ii) -3p2 + 4p + 7
= -3(-2)2 + 4(-2) + 7
= -12 – 8 + 7
= -20 + 7
= -13
(iii) -2p3 – 3p2 + 4p + 7
= -2(-2)3 – 3(-2)2 + 4(-2) + 7
= 16 – 12 – 8 + 7
= 23 – 20
= 3
Question 3.
If a = 2, b = -2, find the value of:
(i) a2 + b2
(ii) a2 + ab + b2
(iii) a2 – b2
Solution:
a = 2, b = -2
(i) a2 + b2
= (2)2 + (-2)2
= 4 + 4
= 8
(ii) a2 + ab + b2
= (2)2 + 2 × (-2) + (-2)2
= 4 – 4 + 4
= 8 – 4
= 4
(iii) a2 – b2
= (2)2 – (-2)2
= 4 – 4
= 0
Question 4.
When a = 0, b = -1, find the value of the given expressions:
(i) 2a2 + b2 + 1
(ii) a2 + ab + 2
(iii) 2a2b + 2ab2 + ab
Solution:
a = 0, b = -1
(i) 2a2 + b2 + 1
= 2(0)2 + (-1)2 + 1
= 0 + 1 + 1
= 2
(ii) a2 + ab + 2
= (0)2 + 0 × (-1) + 2
= 0 + 0 + 2
= 2
(iii) 2a2b + 2ab2 + ab
= 2(0)2(-1) + 2(0)(-1)2 + 0 × (-1)
= 0 + 0 + 0
= 0
Question 5.
If p = -10, find the value of p2 – 2p – 100.
Solution:
p = -10,
p2 – 2p – 100
= (-10)2 – 2(-10) – 100
= 100 + 20 – 100
= 20
Question 6.
If z = 10, find the value of z3 – 3(z – 10).
Solution:
z = 10
z3 – 3(z – 10)
= (10)3 – 3(10 – 10)
= 1000 – 3 × o
= 1000 – 0
= 1000
Question 7.
Simplify the following expressions and find their values when x = 2:
(i) x + 7 + 4(x – 5)
(ii) 3(x + 2) + 5x – 7
(iii) 6x + 5(x – 2)
(iv) 4(2x – 1) + 3x + 11
Solution:
x = 2
(i) x + 7 + 4(x – 5)
= x + 7 + 4x – 20
= 5x – 13
= 5 × 2 – 13
= 10 – 13
= -3
(ii) 3(x + 2) + 5x – 7
= 3x + 6 + 5x – 7
= 8x – 1
= 8(2) – 1
= 16 – 1
= 15
(iii) 6x + 5(x – 2)
= 6x + 5x – 10
= 11x – 10
= 11 × 2 – 10
= 22 – 10
= 12
(iv) 4(2x – 1) + 3x + 11
= 8x – 4 + 3x + 11
= 11x + 7
= 11 × 2 + 7
= 22 + 7
= 29
Question 8.
Simplify the following expressions and find their values when a = -1, b = -2:
(i) 2a – 2b – 4 – 5 + a
(ii) 2(a2 + ab) + 3 – ab
Solution:
a = -1, b = -2
(i) 2a – 2b – 4 – 5 + a
= 3a – 2b – 9
= 3(-1) – 2(-2) – 9
= -3 + 4 – 9
= -12 + 4
= -8
(ii) 2(a2 + ab) + 3 – ab
= 2a2 + 2ab + 3 – ab
= 2a2 + ab + 3
= 2(-1)2 + (-1)(-2) + 3
= 2 × 1 + 2 + 3
= 2 + 2 + 3
= 7