Class 8 Maths

# Algebraic Expression

## NCERT Exercise 9.5

### Part 2

Question 5: Show that.

(i) (3x + 7)^2– 84x = (3x – 7)^2

Answer: LHS = 9x^2 + 42x + 49 - 84x
= 9x^2- 42x + 49
RHS = 9x^2 - 42x + 49
LHS = RHS

(ii) (9p – 5q)^2+ 180pq = (9p + 5q)^2

Answer: LHS = 81p^2 - 90pq + 25q^2+ 180pq
= 81p^2 + 90pq + 25q^2
RHS = 81p^2 + 90pq + 25q^2

(iii) (4/3m-3/4n)^2+2mn=(16)/(9)m^2+(9)/(16)n^2

Answer: (16)/(9)m^2+(9)/(16)n^2-2mn+2mn

=(16)/(9)m^2+(9)/(16)n^2 = RHS proved

(iv) (4pq + 3q)^2– (4pq – 3q)^2= 48pq^2

Answer: = 16p^2q^2 + 24pq^2 + 9q^2 - 16p^2q^2 + 24pq^2- 9q^2
= 48pq^2

(v) (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0

Answer:= a^2 - b^2 + b^2 - c^2 + c^2 - a^2= 0

Question 6: Using identities, evaluate.

(i) 71^2

Answer: 71^2 = (70+1)^2
Using (a + b)^2 = a^2 + 2ab + b^2
= 70^2 + 140 + 1^2
= 4900 + 140 +1= 5041

(ii) 99^2

Answer: = (100 -1)^2
= 100^2 - 200 + 1^2
= 10000 - 200 + 1= 9801

(iii) 102^2

Answer:= (100 + 2)^2
= 100^2 + 400 + 2^2
= 10000 + 400 + 4= 10404

(iv) 998^2

Answer: = (1000 - 2)^2
= 1000^2 - 4000 + 2^2
= 1000000 - 4000 + 4= 996004

(v) 5.2^2

Answer: = (5 + 0.2)^2
= 5^2 + 2 + 0.2^2
= 25 + 2 + 0.4= 27.4

(vi) 297 xx 303

Answer: = (300 - 3 )(300 + 3)
Using (a - b)(a + b) = a^2 - b^2
= 300^2 - 3^2
= 90000 - 9= 89991

(vii) 78 xx 82

Answer: = (80 - 2)(80 + 2)
= 80^2 - 2^2
= 6400 - 4= 6396

(viii) 8.9^2

Answer: = (9 - 0.1)^2
= 9^2 - 1.8 + 0.1^2
= 81 - 1.8 + 0.01= 79.21

(ix) 10.5 xx 9.5

Answer: = (10 + 0.5)(10 - 0.5)
= 10^2 - 0.5^2
= 100 - 0.25= 99.75

Question 7: Using a^2– b^2 = (a + b) (a – b), find

(i) 51^2– 49^2

Answer: = (51 + 49)(51 - 49)
= 100 xx 2= 200

(ii) (1.02)^2– (0.98)^2

Answer:= (1.02 + 0.98)(1.02 - 0.98)
= 2 xx 0.04= 0.08

(iii) 153^2– 147^2

Answer: = (153 + 147)(153 - 147)
= 300 xx 6= 1800

(iv) 12.1^2– 7.9^2

Answer: = (12.1 + 7.9)(12.1 - 7.9)
= 20 xx 4.2= 84

Question 8: Using (x + a) (x + b) = x^2+ (a + b) x + ab, find

(i) 103 xx 104

Answer:= (100 + 3)(100 + 4)
= 100^2 + (3 + 4)100 + 12
= 10000 + 1200 + 12= 11212

(ii) 5.1 xx 5.2

Answer: = (5 + 0.1)(5 + 0.2)
= 5^2 + (0.1+0.2)5 + 0.02
= 25 + 1.5 + 0.02= 26.52

(iii) 103 xx 98

Answer = (100 + 3)(100 - 2)
= 100^2 + (3-2)100 - 6
= 10000 + 100 - 6= 10094

(iv) 9.7 xx 9.8

Answer: = (9 + 0.7 )(9 + 0.8)
= 9^2 + (0.7 + 0.8)9 + 0.63
= 81 + 13.5 + 0.63= 95.13`