NCERT solution class 7 chapter 12 Algebraic expressions 12.3 mathematics

EXERCISE 12.3

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Q 1, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Question 1:

If m = 2, find the value of:
(i) m − 2 (ii) 3m − 5 (iii) 9 − 5m
(iv) 3m² − 2m − 7 (v) 

Answer:

(i) m − 2 = 2 − 2 = 0
(ii) 3m − 5 = (3 × 2) − 5 = 6 − 5 = 1
(iii) 9 − 5m = 9 − (5 × 2) = 9 −10 = −1
(iv) 3m² − 2m − 7 = 3 × (2 × 2) − (2 × 2) − 7
= 12 − 4 − 7 = 1
(v) 

Q 2, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Question 2:

If p = −2, find the value of:
(i) 4p + 7
(ii) −3p² + 4p + 7
(iii) −2p³ − 3p² + 4p + 7

Answer:

(i) 4p + 7 = 4 × (−2) + 7 = − 8 + 7 = −1
(ii) − 3p² + 4p + 7 = −3 (−2) × (−2) + 4 × (−2) + 7
= − 12 − 8 + 7 = −13
(iii) −2p³ − 3p² + 4p + 7
= −2 (−2) × (−2) × (−2) − 3 (−2) × (−2) + 4 × (−2) + 7
= 16 − 12 − 8 + 7 = 3

Q 3, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Question 3:

Find the value of the following expressions, when x = − 1:
(i) 2x − 7 (ii) − x + 2 (iii) x² + 2x + 1
(iv) 2x² − x − 2

Answer:

(i) 2x − 7
= 2 × (−1) − 7 = −9
(ii) − x + 2 = − (−1) + 2 = 1 + 2 = 3
(iii) x² + 2x + 1 = (−1) × (−1) + 2 × (−1) + 1
= 1 − 2 + 1 = 0
(iv) 2x² − x − 2 = 2 (−1) × (−1) − (−1) − 2
= 2 + 1 − 2 = 1

Q 4, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Question 4:

If a = 2, b = − 2, find the value of:
(i) a² + b² (ii) a² + ab + b² (iii) a² − b²

Answer:

(i) a² + b²
= (2)² + (−2)² = 4 + 4 = 8
(ii) a² + ab + b²
= (2 × 2) + 2 × (−2) + (−2) × (−2)
= 4 − 4 + 4 = 4
(iii) a² − b²
= (2)² − (−2)² = 4 − 4 = 0

Question 5:

When a = 0, b = − 1, find the value of the given expressions:
(i) 2a + 2b (ii) 2a² + b² + 1
(iii) 2a² b + 2ab² + ab (iv) a² + ab + 2

Answer:

(i) 2a + 2b = 2 × (0) + 2 × (−1) = 0 − 2 = −2
(ii) 2a² + b² + 1
= 2 × (0)² + (−1) × (−1) + 1
= 0 + 1 + 1 = 2
(iii) 2a²b + 2ab² + ab
= 2 × (0)² × (−1) + 2 × (0) × (−1) × (−1) + 0 × (−1)
= 0 + 0 + 0 = 0
(iv) a² + ab + 2
= (0)² + 0 × (−1) + 2
= 0 + 0 + 2 = 2

Q 6, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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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 −1) + 3x + 11

Answer:

(i) x + 7 + 4 (x − 5) = x + 7 + 4x − 20
= x + 4x + 7 − 20
= 5x − 13
= (5 × 2) − 13
= 10 − 13 = −3
(ii) 3 (x + 2) + 5x − 7 = 3x + 6 + 5x − 7
= 3x + 5x + 6 − 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

Q 7, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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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 = (2 × 3) + 4 = 10
(ii) 2 − 8x + 4x + 4 = 2 + 4 − 8x + 4x
= 6 − 4x = 6 − (4 × 3) = 6 − 12 = −6
(iii) 3a + 5 − 8a + 1 = 3a − 8a + 5 + 1
= − 5a + 6 = −5 × (−1) + 6
= 5 + 6 = 11
(iv) 10 − 3b − 4 − 5b = 10 − 4− 3b − 5b
= 6 − 8b = 6 − 8 × (−2)
= 6 + 16 = 22
(v) 2a − 2b − 4 − 5 + a = 2a + a − 2b − 4 − 5
= 3a − 2b − 9s
= 3 × (−1) − 2 (−2) − 9
= − 3 + 4 − 9 = −8

Q 8, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Question 8:

(i) If z = 10, find the value of z³ − 3 (z − 10).
(ii) If p = − 10, find the value of p² − 2p − 100

Answer:

(i) z³ − 3 (z − 10) = z³ − 3z + 30
= (10 × 10 × 10) − (3 × 10) + 30
= 1000 − 30 + 30 = 1000
(ii) p² − 2p − 100
= (−10) × (−10) − 2 (−10) − 100
= 100 + 20 − 100 = 20

Q 9, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Question 9:

What should be the value of a if the value of 2x² + x − a equals to 5, when x = 0?

Answer:

2x² + x − a = 5, when x = 0
(2 × 0) + 0 − a = 5
0 − a = 5
a = −5

Q 10, Ex 12.3 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Question 10:

Simplify the expression and find its value when a = 5 and b = −3.
2 (a² + ab) + 3 − ab

Answer:

2 (a² + ab) + 3 − ab = 2a² + 2ab + 3 − ab
= 2a² + 2ab − ab + 3
= 2a² + ab + 3
= 2 × (5 × 5) + 5 × (−3) + 3
= 50 − 15 + 3 = 38