Class 7 Maths

# Algebraic Expressions

## Exercise 12.3

Question 1: If m = 2,find the value of:

(i) m – 2

Answer: m – 2 = 2 – 2 = 0

(ii) 3m – 5

Answer: 3m – 5 = 3 × 2 – 5 = 6 – 5 = 1

(iii) 9 – 5m

Answer: 9 – 5m = 9 – 5 × 2 = 9 – 10 = - 1

(iv) 3m^2 – 2m – 7

Answer: 3m^2 – 2m – 7

= 3 × 2^2 – 2 × 2 – 7

= 3 × 4 – 4 – 7

= 12 – 4 – 7 = 12 – 11 = 1

(v) (5m)/(2) – 4

Answer: (5m)/(2) – 4

= 5 × 2 ÷2 – 4 = 5 – 4 = 1

Question 2: If p = - 2, find the value of:

(a) 4p + 7

Answer: 4p + 7 = 4 xx ( - 2) + 7

= - 8 + 7 = - 1

(b) – 3p^2 + 4p + 7

Answer: - 3p^2 + 4p + 7

= - 3 × (- 2)^2 + 4 × ( - 2) + 7

= - 3 × 4 – 8 + 7 = 12 – 8 + 7 = 11

(c) – 2p^3 – 3p^2 + 4p + 7

Answer: - 2p^3 – 3p^2 + 4p + 7

= - 2 × - 2^3 – 3 × (- 2)^2 + 4 × ( - 2) + 7

= (- 2) × ( - 8) – 3 × 4 – 8 + 7

= 16 – 12 – 8 + 7 = 3

Question 3: Find the value of the following expressions, when x = - 1:

(a) 2x – 7

Answer: 2x – 7 = 2 xx ( - 1) – 7

= - 2 – 7 = - 9

(b) – x + 2

Answer: - x + 2 = - ( - 1) + 2 = 1 + 2 = 3

(c) x^2 + 2x + 1

Answer: x^2 + 2x + 1 = - 1^2 + 2 × ( - 1) + 1

= 1 – 2 + 1 = 0

(d) 2x^2 – x – 2

Answer: 2x^2 – x – 2

= 2 × ( - 1)^2 – ( - 1) – 2

= 2 + 1 – 2 = 1

Question 4: If a = 2, b = - 2, find the value of:

(a) a^2 + b^2

Answer: a^2 + b^2 = 2^2 + ( - 2)^2

= 4 + 4 = 8

(b) a^2 + ab + b^2

Answer: a^2 + ab + b^2

= 2^2 + 2 × ( - 2) + ( - 2)^2

= 4 – 4 + 4 = 4

(c) a^2 – b^2

Answer: a^2 – b^2 = 2^2 – ( - 2)^2 = 4 – 4 = 0

Question 5: When a = 0, b = - 1, find the value of the given expressions:

(a) 2a + 2b

Answer: 2a + 2b = 0 + 2 xx ( - 1) = - 2

(b) 2a^2 + b^2 + 1

Answer: 2a^2 + b^2 + 1

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

(c) 2a^2b + 2ab^2 + ab

Answer: 2a^2b + 2ab^2 + ab

= 0 + 0 + 0 = 0

(d) a^2 + ab + 2

Answer: a^2 + ab + 2 = 0 + 0 + 2 = 2

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

(a) x + 7 + 4 (x – 5)

Answer: x+ 7 + 4 (x – 5)

= 2 + 7 + 4 ( 2 – 5)

= 9 + 4 × ( - 3) = 9 – 12 = - 3

(b) 3(x + 2) + 5x – 7

Answer: 3(x + 2) + 5x – 7

= 3 (2 + 2) + 5 × 2 – 7

= 3 × 4 + 10 – 7 = 12 + 3 = 15

(c) 6x + 5(x – 2)

Answer: 6x + 5(x – 2)

= 6 × 2 + 5 ( 2 – 2)

= 12 + 0 = 12

(d) 4(2x – 1) + 3x + 11

Answer: 4(2x – 1) + 3x + 11

= 4 (2 × 2 – 1) + 3 × 2 + 11

= 4 (4 – 1) + 6 + 11

= 4 × 3 + 17 = 12 + 17 = 29