RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.3

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.3 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 12 Algebraic Expressions Ex 12.3

Question 1.
If m = 2, find the value of:
(i) m - 2
Answer:
Value of m - 2 = 2 - 2 = 0

(ii) 3m - 5
Answer:
Value of 3m - 5 = 3 × 2 - 5
= 6 - 5 = 1

(iii) 9 - 5m
Answer:
Value of 9- 5m = 9 - 5 × 2 = 9 - 10 = -1

(iv) 3m² - 2m - 7
Answer:
Value of 3m² - 2m - 7 = 3 × 2² - 2 × 2-7
= 3 × 2 × 2 - 2 × 2 - 7
= 12 - 4 - 7 = 12 - 11 = 1

(v) \(\frac{5 m}{2}\) - 4
Answer:
Value of \(\frac{5 m}{2}\) - 4 = \(\frac{5 \times 2}{2}\) - 4 = \(\frac{10}{2}\) - 2
= 5 - 4 = 1

Question 2.
If p = - 2, find the value of:
(i) 4p + 7
Answer:
Value of 4p + 7= 4 × - 2 + 7 (for p = - 2)

(ii) - 3p² + 4p + 7
Answer:
Value of - 3p² + 4p + 7 (for p = - 2)
= - 3 × (- 2)² + 4 × (- 2) + 7
= - 3 × 4 + 4 × (- 2) + 7
= -12 - 8 + 7
= - 20 + 7 = - 13

(iii) - 2p³ - 3p² + 4p + 7
Answer:
Value of - 2p³ - 3p² + 4p + 7 (for p = - 2)
= -2 × (-2)³ - 3 × (-2)² + 4 × - 2 + 7
= - 2 × (- 2) × (- 2) × (- 2) - 3 × (- 2) × (- 2) + 4 × (- 2) + 7
= 16 - 12 - 8 + 7
= 16 + 7 - 12 - 8
= 23 - 20 = 3

Question 3.
Find the value of the following expressions, when x = - 1:
(i) 2x - 7
Answer:
Value of 2x - 7 (for x = - 1)
= 2 × (- 1) - 7
= - 2 - 7 = - 9

(ii) - x + 2
Answer:
Value of- x + 2 (for x = - 1)
= -(-1) + 2 = 1 + 2 = 3

(iii) x² + 2x + 1
Answer:
Value of x² + 2x + 1 (for x = - 1)
= (- 1)² + 2 × (- 1) + 1
= (- 1) × (- 1) + 2 × (- 1) + 1
= 1 - 2 + 1 = 2 - 2 = 0

(iv) 2x² - x - 2
Answer:
Value of 2x² - x - 2 (for x = - 1)
= 2 × (- 1)² - (- 1) - 2
= 2 × (- 1) × (- 1) + 1 - 2
= 2 + 1 - 2 = 3 - 2 = 1

Question 4.
If a = 2, b = - 2, find the value of:
(i) a² + b²
Answer:
Value of a² + b² (for a = 2, b = - 2)
= (2)² + (-2)²
= 2 × 2 + (-2) × (-2)
= 4 + 4 = 8

(ii) a² + ab + b²
Answer:
Value of a² + ab + b² (for a = 2, b = - 2)
= (2)² + 2 × (- 2) + (- 2)²
= 2 × 2 + 2 × (- 2) + (- 2) × (- 2)
= 4 - 4 + 4 = 0 + 4 = 4

(iii) a² - b²
Answer:
Value of a² - b² (for a = 2, b = -2)
= (2)² - (- 2)² = 2 × 2 - (- 2) × (- 2)
= 4 - 4 = 0

Question 5.
When a = 0, b = - 1, find the value of the given expressions :
(i) 2a + 2b
Answer:
Value of 2a + 2b (for a = 0, b = - 1)
= 2 × 0 + 2 × -1 = 0 - 2 = - 2

(ii) 2a² + b² + 1
Answer:
Value of 2a² + b² + 1 (for a = 0, b = -1)
= 2 × 0 + (- 1) × (- 1) + 1
= 0 + 1 + 1 = 2

(iii) 2a²b + 2ab² + ab
Answer:
Value of 2a²b + 2ab² + ab (for a = 0, b = -1)
= 2 × (0)² × (- 1) + 2 × 0 × (- 1)² + 0 × (- 1)
= 2 × 0 × (-1) + 2 × 0 × (-1) × (-1) + 0 × (-1)
= 0 + 0 + 0 = 0

(iv) a² + ab + 2
Answer:
Value of a² + ab + 2 (for a = 0, b = - 1)
= (0)² + 0 × (- 1) + 2
= 0 × 0 + 0 × (-1) + 2
= 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)
Answer:
x + 7 + 4(x - 5)
= x + 7 + 4 × x -4 × 5
= x + 7 + 4 × -20
= (x + 4x) + (7 - 20)
= 5x - 13

Value of 5x - 13 (for x = 2)
= 5 × 2 -13
= 10 - 13 = -3

(ii) 3(x + 2) + 5x - 7
Answer:
3(x + 2) + 5x - 7
= 3 × x + 3 × 2 + 5x - 7
= 3x + 6 + 5x - 7
= (3x + 5x) + (6 - 7)
= 8x - 1

Value of 8x - 1 (for x = 2)
= 8 × 2 - 1
= 16 - 1 = 15

(iii) 6x + 5 (x - 2)
Answer:
6x + 5 (x - 2) = 6x + 5 × x + 5 × (- 2)
= 6x + 5x - 10 = 11x - 10

Value of 11x - 10 (for x = 2)
= 11 × 2 - 10 = 22 - 10 = 12

(iv) 4(2x - 1) + 3x + 11
Answer:
4(2x - 1) + 3x + 11 = 4 × 2x - 4 × 1 + 3x + 11
= 8x - 4 + 3x + 11
= (8x + 3x) + (-4 + 11) = 11x + 7

Value of 11x + 7 (for x = 2)
= 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
Answer:
3x - 5 - x + 9 = (3x - x) + (- 5 + 9)
= 2x + 4

Value of 2x + 4 (for x = 3)
= 2 × 3 + 4
= 6 + 4 = 10

(ii) 2 - 8x + 4x + 4
Answer:
2 - 8x + 4x + 4
= (2 + 4) + (-8x + 4x)
= 6 - 4x

Value of 6 - 4x (for x - 3)
= 6 - 4 × 3
= 6 - 12 = -6

(iii) 3o + 5 - 8a + 1
Answer:
3a + 5 - 8a + 1 = (3a - 8a) + (5 + 1)
= - 5a + 6

Value of -5a + 6 = - 5 × (- 1) + 6 (for a = - 1)
= 5 + 6 = 11

(iv) 10 - 3b - 4 - 5b
Answer:
10 - 3b - 4 - 5b = (10 - 4) + (- 3b - 5b) = b +(-8b)
= b - 8b

Value of b - 8b (for b = - 2) = 6 - 8 × (- 2)
= 6 + 16 = 22

(v) 2a - 2b - 4 - 5 + a
Answer:
2a - 2b - 4 - 5 + a = (2a + a) - 2b + (-4 - 5)
= 3a - 2b - 9

Value of 3a - 2b - 9 (for a = - 1, b = - 2)
= 3 ×- 1-2 × -2 - 9 = -3 + 4 - 9
= -3 - 9 + 4
= -12 + 4 = -8

Question 8.
(i) If z = 10, find the value of z³ - 3(z -10).
Answer:
z³ - 3(z - 10) = z³ - 3xz - 3 x (-10)
= z³ - 3xz - 3X(- 10)
= z³ - 3z + 30

Value of z³ - 3z + 30 (for z = 10)
= (10)3 - 3 × 10 + 30
= 10 × 10 × 10-30 + 30
= 1000 - 30 + 30 = 1000 + 0 = 1000

(ii) If p = - 10, find the value of p² - 2p - 100.
Answer:
Value of p² - 2p - 100 (for p = -10)
= (- 10)² - 2 × (- 10) - 100
= (-10) × (-10) - 2 × (-10) - 100
= 100 + 20 - 100
= 100 - 100 + 20
= 0 + 20 = 20

Question 9.
What should be the value of a if the value of 2x² + x - a equals to 5, when x = 0?
Answer:
Value of 2x² + x - a (for x = 0)
= 2 × (0)² + 0 - a
= 2 × 0 + 0 - a
= 0 + 0 - a = -a
But given value of 2x² + x - a, at x = 0 equals to 5.
∴ - a = 5 ⇒ a = - 5.

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-a6 = 2a² + 2ab + 3 - ab
= 2a² + 2ab + 3 - ab
= 2a² + (2ab - ab) + 3
= 2a² + ab + 3

Value of 2a² + ab + 3(for a = 5, b = - 3)
= 2 × (5)² + 5 × (- 3) + 3
= 2 × 5 × 5 + 5 × (-3) + 3
= 50 - 15 + 3
= 35 + 3 = 38