## 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) 3m^{2} – 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) 3m^{2} – 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) -3p^{2} + 4p + 7

(iii) -2p^{3} – 3p^{2} + 4p + 7

Solution:

p = -2

(i) 4p + 7

= 4 × (-2) + 7

= -8 + 7

= -1

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

= -3(-2)^{2} + 4(-2) + 7

= -12 – 8 + 7

= -20 + 7

= -13

(iii) -2p^{3} – 3p^{2} + 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) a^{2} + b^{2}

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

(iii) a^{2} – b^{2}

Solution:

a = 2, b = -2

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

= (2)^{2} + (-2)^{2}

= 4 + 4

= 8

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

= (2)^{2} + 2 × (-2) + (-2)^{2}

= 4 – 4 + 4

= 8 – 4

= 4

(iii) a^{2} – b^{2}

= (2)^{2} – (-2)^{2}

= 4 – 4

= 0

Question 4.

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

(i) 2a^{2} + b^{2} + 1

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

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

Solution:

a = 0, b = -1

(i) 2a^{2} + b^{2} + 1

= 2(0)^{2} + (-1)^{2} + 1

= 0 + 1 + 1

= 2

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

= (0)^{2} + 0 × (-1) + 2

= 0 + 0 + 2

= 2

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

= 2(0)^{2}(-1) + 2(0)(-1)^{2} + 0 × (-1)

= 0 + 0 + 0

= 0

Question 5.

If p = -10, find the value of p^{2} – 2p – 100.

Solution:

p = -10,

p^{2} – 2p – 100

= (-10)^{2} – 2(-10) – 100

= 100 + 20 – 100

= 20

Question 6.

If z = 10, find the value of z^{3} – 3(z – 10).

Solution:

z = 10

z^{3} – 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(a^{2} + 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(a^{2} + ab) + 3 – ab

= 2a^{2} + 2ab + 3 – ab

= 2a^{2} + ab + 3

= 2(-1)^{2} + (-1)(-2) + 3

= 2 × 1 + 2 + 3

= 2 + 2 + 3

= 7