These NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.3 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.3

Question 1.

If m – 2, find the value of:

(i) m – 2

(ii) 3m – 5

(iii) 9 – 5m

(iv) 3m^{2} – 2m – 7

(v) \(\frac { 5m }{ 2 }\) – 4

Answer:

(i) m- 2 = 2 – 2 (m = = 2)

= 0

(ii) 3m – 5 = 3 (2) – 5 (m = – 2)

= 6 – 5 = 1

(iii) 9 – 5m = 9 – 5(2) (m = = 2)

= 9- 10

= -1

(iv) 3m^{2} – 2m – 7

= 3 (2)^{2} – 2(2) – 7

(m = 2)

= 3 (4) – 4 – 7

= 12 – 4 – 7

= 12 – 11

= 1

(v) \(\frac { 5m }{ 2 }\) – 4 = \(\frac{5(2)}{2}\) – 4 (m = 2)

= 5 – 4

= 1

Question 2.

If p = -2, find the value of:

(i) 4p + 7

(ii) – 3p^{2} + 4p + 7

(iii) – 2p^{2} – 3p^{2} + 4p + 7

Answer:

(i) 4p + 7 = 4(-2) + 7

= – 8 + 7 = -1

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

= – 3 (-2)^{2} + 4(-2) + 7

(when p = -2)

= – 3 (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

(when p = -2)

= – 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

(ii) -x + 2

(iii) x^{2} + 2x + 1

(iv) 2x^{2} – x -2

Answer:

(i) 2x – 7 = 2(-1) – 7 (whenx = -1)

= -2 – 7 = -9

(ii) -x + 2 = -(-1) + 2 (When x = -1)

= 1 + 2 = 3

(iii) x^{2} + 2x + 1 = (-1)^{2} + 2 (-1) + 1

(When x = – 1)

= 1 – 2 + 1

= 2 – 2 = 0

(iv) 2x^{2} – x – 2 =2 (-1)^{2} – (-1) – 2

(When x = -1)

= 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:

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

(When a = 2, b = -2)

= 4 + 4 = 8

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

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

(When a = 2, b = – 2)

= 4 – 4 + 4

= 8 – 4 = 4

(iii) a2 – b2 = 22 – (-2)2

(When a = 2, b = -2) = 4-(4) = 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:

(i) 2a + 2b = 2 (0) + 2(—1)

(When a = 0, b = -1)

= 0 – 2 = -2

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

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

(When a = 0, b = -1)

= 0 + (1) + (1)

= 1 + 1 = 2

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

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

(When a = 0, b = -1)

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

= 0 + 0 + 0

= 0

(iv) a^{2} + ab + 2 = (0)^{2} + 0 (-1) + 2

(When 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 – l) + 3x+ 11

Answer:

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

= x + 7 + 4x – 20

= x + 4x + 7 – 20

= 5x – 13 (When x = 2)

= 5 (2) – 13

= 10- 13

= -3

(ii) 3 (x + 2) + 5x – 7 = 3x + 6 + 5x – 7

= 3x + 5x + 6 – 7

= 8x – 1 (When x = 2)

= 16 – 1 = 15

(iii) 6x + 5 (x – 2) = 6x + 5x – 10

= 1 lx – 10 (When x = 2)

= 11 (2) – 10 = 22-

= 12

(iv) 4(2x – 1)+ 3x + 11

= 8x + 3x – 4 + 11

= 8x + 3x + 11 – 4

= 11x + 7 (When x = 2)

h = 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

(ii) 2 – 8x + 4x + 4

(iii) 3a + 5 – 8a + 1

(iv) 10 – 3b – 4 – 5b

(v) 2a – 2b – 4 – 5 + a

Answer:

(i) 3x-5-x + 9

= 3x-x-5 + 9

= 2x + 4 (When x = 3)

= 2(3)+ 4

= 6 + 4

= 10

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

= -8x + 4x + 4 + 2

= (- 8 + 4) x + 6

= – 4x + 6

(When x = 3)

= – 4(3) + 6

= -12+ 6 =-6

(iii) 3a + 5 – 8a + 1

= 3a – 8a + 5 + 1

= (3 – 8) a + 6

= -5a + 6

(When a = – 1)

= -5 (-1) + 6

= 5 + 6= 11

(iv) 10 – 3b – 4 – 5b = -3b -5b +10-4

= (-3 -5) b + 6 = – 8 b + 6

(When b = – 2) = – 8 (-2) + 6

= 16 + 6 = 22

(v) 2a – 2b – 4 – 5 + a =

2a + a – 2b – 4 -5 = 3a – 2b – 9

(When a = – 1 and b = -2) = 3 (-1) -2 (-2) -9 = -3 + 4 -9 = -12+ 4 =-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:

(i) z^{3} – 3 [z – 10] = 10^{2} – 3 [10- 10]

(When z = 10)

= 1000 – 3 (0)= 1000

(ii) p^{2} – 2p – 100

= (-10)^{2} – 2 (-10) – 100

(When p = -10)

= 100 + 20 – 100

= 120 – 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? Ans: 2x^{2}+ x – a = 5 (Given: x = 0)

2(0)^{2} + 0 – a = 5

0 + 0 – a = 5

-a =5

a = – 5

The value of a = – 5

Question 10.

Simplify the expression and find its value when a = 5 and b = – 3.

2(a^{2} + ab) + 3 – ab

Answer:

2(a^{2} + ab) + 3 – ab

= 2 [5^{2} + 5(-3)] + 3 -(5) (-3)

= 2 [25- 15] +3 + 15

= 2(10) + 18

= 20 + 18 = 38