Algebraic Expressions and Identities - Solutions 5
CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 9
Algebraic Expressions and Identities (Ex. 9.5)
NCERT Solutions
CHAPTER - 9
Algebraic Expressions and Identities (Ex. 9.5)
1. Use a suitable identity to get each of the following products:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
(viii) 
(ix) 
(x) 
Ans. (i) 
[Using identity 
]
]
= 
(ii) 
= 
[Using identity ]
]
= 
(iii) 
= 
[Using identity 
]
]
= 
(iv) 
= 
[Using identity ]
]
= 
(v) 
[Using identity 
]
]
= 
(vi) 
= 
[Using identity 
]
]
= 
(vii) 
[Using identity ]
]
= 
(viii) 
= 
[Using identity ]
]
= 
(ix) 
= 
[Using identity ]
]
= 
(x) 
= 
[Using identity ]
]
= 
2. Use the identity 
to find the following products:
to find the following products:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
Ans. (i) 
[Using identity ]
]
= 
(ii) 
[Using identity ]
]
= 
(iii)
= 
[Using identity ]
]
= 
(iv) 
=(4x)2+{5+(-1)}(4x)+(5)(-1)
[Using identity ]
]
= 
= 
= 
(v) 
[Using identity ]
]
= 
= 
(vi)
[Using identity ]
]
= 
= 
(vii) 
[Using identity ]
]
= 
3. Find the following squares by using identities:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
Ans. (i) 
[Using identity 
]
]
= 
(ii) 
[Using identity ]
]
= 
(iii)
[Using identity ]
]
= 
(iv)
[Using identity ]
]
= 
(v)
[Using identity ]
]
= 
(vi)
[Using identity ]
]
= 
4. Simplify:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
Ans. (i) 
[Using identity ]
]
= 
(ii) 
={(2x+5)+(2x-5)}{(2x+5)-(2x-5)}
[Using identity (a2-b2)=(a+b)(a-b)]
={4x}{2x+5-2x+5}
=(4x)(10)
=40x
(iii) 
[Using identities and ]
and ]
=
=
= 
(iv) 
[Using identity ]
]
= 
= 
= 
(v) 
[Using identity ]
=
= 
= 
(vi) 
[Using identity ]
]
= 
= 
(vii) 
= 
[Using identity ]
]
= 
= 
5. Show that:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Ans. (i) L.H.S. = 
[Using identity ]
]
= 
= 
= 
[
]
[]
= R.H.S.
(ii) L.H.S. = 
[Using identity ]
]
= 
= 
= 
[]
[]
(iii) L.H.S. = 
[Using identity ]
]
= 
= 
= R.H.S.
(iv) L.H.S. = 
= 
[Using identities and ]
[Using identities and ]
= 
= 
= 
= =
= R.H.S.
(v)L.H.S.= 
= 
=
[Using identity 
]
]
= 0
= R.H.S.
6. Using identities, evaluate:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
(viii) 
(ix) 10.5 9.5
Ans. (i) 
[Using identity 
]
]
= 4900 + 140 + 1 = 5041
(ii) 
[Using identity ]
]
= 10000 – 200 + 1 = 9801
(iii) 
[Using identity ]
]
= 10000 + 400 + 4 = 10404
(iv) 
[Using identity ]
]
= 1000000 – 4000 + 4 = 996004
(v) 
[Using identity ]
]
= 25 + 2.0 + 0.04 = 27.04
(vi)
= 
= 
[Using identity ]
]
= 90000 – 9 = 89991
(vii) 
= 
=
= 
[Using identity ]
]
= 6400 – 4 = 6396
(viii) 
[Using identity ]
]
= 64 + 14.4 + 0.81 = 79.21
(ix) 10.5 x 9.5 = 
= 
[Using identity ]
]
= 100 – 0.25 = 99.75
7. Using 
find
find
(i) 
(ii) 
(iii) 
(iv) 
Ans. (i) 
[Using identity 
]
]
= 
= 200
= 200
(ii)
[Using identity ]
]
= 
= 0.08
= 0.08
(iii) 
[Using identity ]
]
= 
= 1800
= 1800
(iv) 
[Using identity 
]
]
= 
= 84.0 = 84
= 84.0 = 84
8. Using 
, find
, find
(i) 
(ii) 
(iii) 
(iv) 
Ans. (i) 
= 
=
= 
[Using identity ]
]
= 
= 10000 + 700 + 12 = 10712
(ii) 
= 
[Using identity ]
]
= 
= 25 + 1.5 + 0.02 = 26.52
(iii) 
= 
[Using identity ]
]
= 
= 10000 + 100 – 6 = 10094
(iv) 
= 
[Using identity ]
[Using identity ]
= 
= 
= 100 – 5 + 0.06 = 95.06
