NCERT Solutions for Class 7 Maths Exercise 12.3 Chapter 12 Algebraic Expressions in simple PDF are available here. This exercise of NCERT Solutions Maths for Class 7 Chapter 12 contains topics related to finding the value of an expression. PDFs are very useful to help students understand the question pattern and different types of problems. It is essential to understand the various kinds of problems and figure out the best solutions for them. Students can find NCERT Solutions for Class 7 Maths where students can understand the fastest way to solve.

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**1. If m = 2, find the value of:**

**(i) m â€“ 2 **

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= 2 -2

= 0

**(ii) 3m â€“ 5**

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= (3 Ã— 2) â€“ 5

= 6 â€“ 5

= 1

**(iii) 9 â€“ 5m**

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= 9 â€“ (5 Ã— 2)

= 9 â€“ 10

= â€“ 1

**(iv) 3m ^{2} â€“ 2m â€“ 7 **

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= (3 Ã— 2^{2}) â€“ (2 Ã— 2) â€“ 7

= (3 Ã— 4) â€“ (4) â€“ 7

= 12 â€“ 4 -7

= 12 â€“ 11

= 1

**(v) (5m/2) â€“ 4**

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= ((5 Ã— 2)/2) â€“ 4

= (10/2) â€“ 4

= 5 â€“ 4

= 1

**2. If p = â€“ 2, find the value of:**

**(i) 4p + 7 **

**Solution:-**

From the question it is given that p = -2

Then, substitute the value of p in the question

= (4 Ã— (-2)) + 7

= -8 + 7

= -1

**(ii) â€“ 3p ^{2} + 4p + 7**

**Solution:-**

From the question it is given that p = -2

Then, substitute the value of p in the question

= (-3 Ã— (-2)^{2}) + (4 Ã— (-2)) + 7

= (-3 Ã— 4) + (-8) + 7

= -12 â€“ 8 + 7

= -20 + 7

= -13

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**(iii) â€“ 2p ^{3} â€“ 3p^{2} + 4p + 7**

**Solution:-**

From the question it is given that p = -2

Then, substitute the value of p in the question

= (-2 Ã— (-2)^{3}) â€“ (3 Ã— (-2)^{2}) + (4 Ã— (-2)) + 7

= (-2 Ã— -8) â€“ (3 Ã— 4) + (-8) + 7

= 16 â€“ 12 â€“ 8 + 7

= 23 â€“ 20

= 3

**3. Find the value of the following expressions, when x = â€“1:**

**(i) 2x â€“ 7**

**Solution:-**

From the question it is given that x = -1

Then, substitute the value of x in the question

= (2 Ã— -1) â€“ 7

= â€“ 2 â€“ 7

= â€“ 9

**(ii) â€“ x + 2**

**Solution:-**

From the question it is given that x = -1

Then, substitute the value of x in the question

= â€“ (-1) + 2

= 1 + 2

= 3

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

**Solution:-**

From the question it is given that x = -1

Then, substitute the value of x in the question

= (-1)^{2} + (2 Ã— -1) + 1

= 1 â€“ 2 + 1

= 2 â€“ 2

= 0

**(iv) 2x ^{2} â€“ x â€“ 2**

**Solution:-**

From the question it is given that x = -1

Then, substitute the value of x in the question

= (2 Ã— (-1)^{2}) â€“ (-1) â€“ 2

= (2 Ã— 1) + 1 â€“ 2

= 2 + 1 â€“ 2

= 3 â€“ 2

= 1

**4. If a = 2, b = â€“ 2, find the value of:**

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

**Solution:-**

From the question it is given that a = 2, b = -2

Then, substitute the value of a and b in the question

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

= 4 + 4

= 8

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

**Solution:- **

From the question it is given that a = 2, b = -2

Then, substitute the value of a and b in the question

= 2^{2} + (2 Ã— -2) + (-2)^{2}

= 4 + (-4) + (4)

= 4 â€“ 4 + 4

= 4

**(iii) a ^{2} â€“ b^{2}**

**Solution:-**

From the question it is given that a = 2, b = -2

Then, substitute the value of a and b in the question

= 2^{2} â€“ (-2)^{2}

= 4 â€“ (4)

= 4 â€“ 4

= 0

**5. When a = 0, b = â€“ 1, find the value of the given expressions:**

**(i) 2a + 2b **

**Solution:-**

From the question it is given that a = 0, b = -1

Then, substitute the value of a and b in the question

= (2 Ã— 0) + (2 Ã— -1)

= 0 â€“ 2

= -2

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

**Solution:-**

From the question it is given that a = 0, b = -1

Then, substitute the value of a and b in the question

= (2 Ã— 0^{2}) + (-1)^{2} + 1

= 0 + 1 + 1

= 2

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

**Solution:-**

From the question it is given that a = 0, b = -1

Then, substitute the value of a and b in the question

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

= 0 + 0 +0

= 0

**(iv) a ^{2} + ab + 2**

**Solution:-**

From the question it is given that a = 0, b = -1

Then, substitute the value of a and b in the question

= (0^{2}) + (0 Ã— (-1)) + 2

= 0 + 0 + 2

= 2

**6. Simplify the expressions and find the value if x is equal to 2**

**(i) x + 7 + 4 (x â€“ 5)**

**Solution:-**

From the question it is given that x = 2

We have,

= x + 7 + 4x â€“ 20

= 5x + 7 â€“ 20

Then, substitute the value of x in the equation

= (5 Ã— 2) + 7 â€“ 20

= 10 + 7 â€“ 20

= 17 â€“ 20

= â€“ 3

**(ii) 3 (x + 2) + 5x â€“ 7**

**Solution:-**

From the question it is given that x = 2

We have,

= 3x + 6 + 5x â€“ 7

= 8x â€“ 1

Then, substitute the value of x in the equation

= (8 Ã— 2) â€“ 1

= 16 â€“ 1

= 15

**(iii) 6x + 5 (x â€“ 2) **

**Solution:-**

From the question it is given that x = 2

We have,

= 6x + 5x â€“ 10

= 11x â€“ 10

Then, substitute the value of x in the equation

= (11 Ã— 2) â€“ 10

= 22 â€“ 10

= 12

**(iv) 4(2x â€“ 1) + 3x + 11**

**Solution:-**

From the question it is given that x = 2

We have,

= 8x â€“ 4 + 3x + 11

= 11x + 7

Then, substitute the value of x in the equation

= (11 Ã— 2) + 7

= 22 + 7

= 29

**7. Simplify these expressions and find their values if x = 3, a = â€“ 1, b = â€“ 2.**

**(i) 3x â€“ 5 â€“ x + 9**

**Solution:-**

From the question it is given that x = 3

We have,

= 3x â€“ x â€“ 5 + 9

= 2x + 4

Then, substitute the value of x in the equation

= (2 Ã— 3) + 4

= 6 + 4

= 10

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**(ii) 2 â€“ 8x + 4x + 4**

**Solution:-**

From the question it is given that x = 3

We have,

= 2 + 4 â€“ 8x + 4x

= 6 â€“ 4x

Then, substitute the value of x in the equation

= 6 â€“ (4 Ã— 3)

= 6 â€“ 12

= â€“ 6

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**(iii) 3a + 5 â€“ 8a + 1 **

**Solution:-**

From the question it is given that a = -1

We have,

= 3a â€“ 8a + 5 + 1

= â€“ 5a + 6

Then, substitute the value of a in the equation

= â€“ (5 Ã— (-1)) + 6

= â€“ (-5) + 6

= 5 + 6

= 11

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**(iv) 10 â€“ 3b â€“ 4 â€“ 5b**

**Solution:-**

From the question it is given that b = -2

We have,

= 10 â€“ 4 â€“ 3b â€“ 5b

= 6 â€“ 8b

Then, substitute the value of b in the equation

= 6 â€“ (8 Ã— (-2))

= 6 â€“ (-16)

= 6 + 16

= 22

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**(v) 2a â€“ 2b â€“ 4 â€“ 5 + a**

**Solution:-**

From the question it is given that a = -1, b = -2

We have,

= 2a + a â€“ 2b â€“ 4 â€“ 5

= 3a â€“ 2b â€“ 9

Then, substitute the value of a and b in the equation

= (3 Ã— (-1)) â€“ (2 Ã— (-2)) â€“ 9

= -3 â€“ (-4) â€“ 9

= â€“ 3 + 4 â€“ 9

= -12 + 4

= -8

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**8. (i) If z = 10, find the value of z ^{3} â€“ 3(z â€“ 10).**

**Solution:-**

From the question it is given that z = 10

We have,

= z^{3} â€“ 3z + 30

Then, substitute the value of z in the equation

= (10)^{3} â€“ (3 Ã— 10) + 30

= 1000 â€“ 30 + 30

= 1000

**(ii) If p = â€“ 10, find the value of p ^{2} â€“ 2p â€“ 100**

**Solution:-**

From the question it is given that p = -10

We have,

= p^{2} â€“ 2p â€“ 100

Then, substitute the value of p in the equation

= (-10)^{2} â€“ (2 Ã— (-10)) â€“ 100

= 100 + 20 â€“ 100

= 20

**9. What should be the value of a if the value of 2x ^{2} + x â€“ a equals to 5, when x = 0?**

**Solution:-**

From the question it is given that x = 0

We have,

2x^{2} + x â€“ a = 5

a = 2x^{2} + x â€“ 5

Then, substitute the value of x in the equation

a = (2 Ã— 0^{2}) + 0 â€“ 5

a = 0 + 0 â€“ 5

a = -5

**10. Simplify the expression and find its value when a = 5 and b = â€“ 3.**

**2(a ^{2} + ab) + 3 â€“ ab**

**Solution:-**

From the question it is given that a = 5 and b = -3

We have,

= 2a^{2} + 2ab + 3 â€“ ab

= 2a^{2} + ab + 3

Then, substitute the value of a and b in the equation

= (2 Ã— 5^{2}) + (5 Ã— (-3)) + 3

= (2 Ã— 25) + (-15) + 3

= 50 â€“ 15 + 3

= 53 â€“ 15

= 38

Very good explanation.