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:

(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
]


=



=



= 

(iv) 


[Using identity
]

= 

= 

= 

(v) 



=

= 

= 

(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
]



=
=
= 



= 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

(i)

(ii) 

(iii)

(iv) 

Ans. (i)

[Using identity
]

=
= 200

(ii) 


[Using identity
]

=
= 0.08

(iii)

[Using identity
]

=
= 1800

(iv)

[Using identity
]

=
= 84.0 = 84

8. Using
, 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
]


= 

= 

= 100 – 5 + 0.06 = 95.06