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Page 1
Chapter 6: Algebraic Expressions
Page No: 99
Exercise 6A
Question 1:
Solution:
( ) Required sum = (5 7 6 )
= (12 6 )
= 6
i x x x
xx
x
??
?
3 2 4
( ) Required sum =
5 3 5
9 10 12
=
15
7
=
15
ii x x x
x x x
x
?
??
??
2 2 2
2 2 2
2
(iii) Required sum = 5 ( 8 ) 7
= 5 8 7
= 4
a b a b a b
a b a b a b
ab
? ? ?
??
2 2 2 2
2 2 2
2 2 2
31
(iv) Required sum = 5 ( 3 ) ( )
44
31
= 5 3
44
15
= 2 =
22
x x x x
x x x x
x x x
? ? ? ? ?
? ? ?
?
(v) Required sum = 3 4 2 8 5 2 3
= 2 5 3 2 4 8 3
= 4 4 7
x y z y x z x y z
x x x y y y z z z
x y z
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
??
2 2 2 2 2 2
2 2 2 2 2 2
(vi) Required sum = Collecting like term and adding them
= 2 3 5 6 ( 3 4 )
= 2 5 3 3 6 4
= 4
x y x y x y
x x x y y y
x
? ? ? ? ? ?
? ? ? ? ?
22
y ?
2 2 2
2
(vii) Collecting like terms and adding them:
= 5 2 8 8 7 9 3 7 2
= 13 4 14
x x x x x x
xx
? ? ? ? ? ? ? ?
??
? ?
3 2 4 2 3 4 3 7
3 2 3 2 1
()
4 3 4 3 2
ab a b a a b b a b
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
1
Page 2
Chapter 6: Algebraic Expressions
Page No: 99
Exercise 6A
Question 1:
Solution:
( ) Required sum = (5 7 6 )
= (12 6 )
= 6
i x x x
xx
x
??
?
3 2 4
( ) Required sum =
5 3 5
9 10 12
=
15
7
=
15
ii x x x
x x x
x
?
??
??
2 2 2
2 2 2
2
(iii) Required sum = 5 ( 8 ) 7
= 5 8 7
= 4
a b a b a b
a b a b a b
ab
? ? ?
??
2 2 2 2
2 2 2
2 2 2
31
(iv) Required sum = 5 ( 3 ) ( )
44
31
= 5 3
44
15
= 2 =
22
x x x x
x x x x
x x x
? ? ? ? ?
? ? ?
?
(v) Required sum = 3 4 2 8 5 2 3
= 2 5 3 2 4 8 3
= 4 4 7
x y z y x z x y z
x x x y y y z z z
x y z
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
??
2 2 2 2 2 2
2 2 2 2 2 2
(vi) Required sum = Collecting like term and adding them
= 2 3 5 6 ( 3 4 )
= 2 5 3 3 6 4
= 4
x y x y x y
x x x y y y
x
? ? ? ? ? ?
? ? ? ? ?
22
y ?
2 2 2
2
(vii) Collecting like terms and adding them:
= 5 2 8 8 7 9 3 7 2
= 13 4 14
x x x x x x
xx
? ? ? ? ? ? ? ?
??
? ?
3 2 4 2 3 4 3 7
3 2 3 2 1
()
4 3 4 3 2
ab a b a a b b a b
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
1
( ) Collecting like terms and adding them:
2 4 3 3 5 2 5 7 5
= ( )
3 5 5 4 2 3 2 4 6
2 3 5 4 5 7 3 2 5
= ( ) ( ) ( )
3 4 2 5 2 4 5 3 6
(8 9 30) ( 16 50 35) (18 20 25)
=
12 20 3
viii
a b c a b c a b c
a a a b b b c c c
a b c
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
??
0
29 31 13
=
12 20 30
a b c ??
( x) Collecting like terms and adding them:
8 11 9 3 5 9
= ( )
5 7 4 2 3 5
8 3 11 5 9 9
=
5 2 7 3 4 5
1 2 9
=
10 21 20
i
x y xy x y xy
x x y y xy xy
x y xy
? ? ? ? ? ?
? ? ? ? ?
??
3 2 3 2 2
3 3 2 2 2
32
(x) Collecting like terms and adding them:
3 1 5 5 3 1 3 8
= ( ) ( )
2 4 3 4 5 5 8 15
3 5 1 3 3 5 1 8
=
2 4 4 5 8 3 5 15
1 13 5 4
=
4 20 8 3
x x x x x x x
x x x x x x x
x x x
? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ?
Question 2:
Solution:
( ) 7 ( 8 )
= 7 8
= 15
i xy xy
xy xy
xy
??
?
22
2
(ii) 3
= 4
xx
x
??
?
(iii) (4 5 ) ( )
= 4 5
= 5 6
y x x y
y x x y
yx
? ? ?
? ? ?
?
2 2 2 2
2 2 2 2
(iv) ( 2 ) ( 2 )
= 2 2 (collecting like terms and adding them)
= 4
a b ab a b ab
a a b b ab ab
ab
? ? ? ? ?
? ? ? ? ?
2 2 2 2
2 2 2 2
22
(v) (2 3 +6 ) ( )
= 2 3 6 (collecting like terms and adding them)
= 2 6
x y xy x y
x x y y xy
x y xy
? ? ?
? ? ? ?
??
2
Page 3
Chapter 6: Algebraic Expressions
Page No: 99
Exercise 6A
Question 1:
Solution:
( ) Required sum = (5 7 6 )
= (12 6 )
= 6
i x x x
xx
x
??
?
3 2 4
( ) Required sum =
5 3 5
9 10 12
=
15
7
=
15
ii x x x
x x x
x
?
??
??
2 2 2
2 2 2
2
(iii) Required sum = 5 ( 8 ) 7
= 5 8 7
= 4
a b a b a b
a b a b a b
ab
? ? ?
??
2 2 2 2
2 2 2
2 2 2
31
(iv) Required sum = 5 ( 3 ) ( )
44
31
= 5 3
44
15
= 2 =
22
x x x x
x x x x
x x x
? ? ? ? ?
? ? ?
?
(v) Required sum = 3 4 2 8 5 2 3
= 2 5 3 2 4 8 3
= 4 4 7
x y z y x z x y z
x x x y y y z z z
x y z
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
??
2 2 2 2 2 2
2 2 2 2 2 2
(vi) Required sum = Collecting like term and adding them
= 2 3 5 6 ( 3 4 )
= 2 5 3 3 6 4
= 4
x y x y x y
x x x y y y
x
? ? ? ? ? ?
? ? ? ? ?
22
y ?
2 2 2
2
(vii) Collecting like terms and adding them:
= 5 2 8 8 7 9 3 7 2
= 13 4 14
x x x x x x
xx
? ? ? ? ? ? ? ?
??
? ?
3 2 4 2 3 4 3 7
3 2 3 2 1
()
4 3 4 3 2
ab a b a a b b a b
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
1
( ) Collecting like terms and adding them:
2 4 3 3 5 2 5 7 5
= ( )
3 5 5 4 2 3 2 4 6
2 3 5 4 5 7 3 2 5
= ( ) ( ) ( )
3 4 2 5 2 4 5 3 6
(8 9 30) ( 16 50 35) (18 20 25)
=
12 20 3
viii
a b c a b c a b c
a a a b b b c c c
a b c
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
??
0
29 31 13
=
12 20 30
a b c ??
( x) Collecting like terms and adding them:
8 11 9 3 5 9
= ( )
5 7 4 2 3 5
8 3 11 5 9 9
=
5 2 7 3 4 5
1 2 9
=
10 21 20
i
x y xy x y xy
x x y y xy xy
x y xy
? ? ? ? ? ?
? ? ? ? ?
??
3 2 3 2 2
3 3 2 2 2
32
(x) Collecting like terms and adding them:
3 1 5 5 3 1 3 8
= ( ) ( )
2 4 3 4 5 5 8 15
3 5 1 3 3 5 1 8
=
2 4 4 5 8 3 5 15
1 13 5 4
=
4 20 8 3
x x x x x x x
x x x x x x x
x x x
? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ?
Question 2:
Solution:
( ) 7 ( 8 )
= 7 8
= 15
i xy xy
xy xy
xy
??
?
22
2
(ii) 3
= 4
xx
x
??
?
(iii) (4 5 ) ( )
= 4 5
= 5 6
y x x y
y x x y
yx
? ? ?
? ? ?
?
2 2 2 2
2 2 2 2
(iv) ( 2 ) ( 2 )
= 2 2 (collecting like terms and adding them)
= 4
a b ab a b ab
a a b b ab ab
ab
? ? ? ? ?
? ? ? ? ?
2 2 2 2
2 2 2 2
22
(v) (2 3 +6 ) ( )
= 2 3 6 (collecting like terms and adding them)
= 2 6
x y xy x y
x x y y xy
x y xy
? ? ?
? ? ? ?
??
2
(vi) (2 3 ) ( 3 )
= 2 3 3 (collecting like terms and adding them)
= 2 2
z x y x y z
z z x x y y
z x y
? ? ? ? ?
? ? ? ? ?
? ? ?
Question 3:
Solution:
? ?
? ?
Required sum = ( 3 4 ) (4 9 ) ( 2 3 ) (2 3 4 )
= 4 8 2 3 4
= 2 3 4
a b c a b c b c a a b c
a c a b c
a b c
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ?
??
Question 4:
Solution:
22
22
2
22
22
2
22
2
(8 7 6 ) ( 3 4 )
= 8 3 7 4 6
5 11 5
(2 4 3 ) ( )
2 4 3
3 4
Now,
( 3 4 ) (5 11 5 )
4 14 9
m n p m n p
m m n n p p
m n p
m n p m n p
m m n n p p
m n p
m n p m n p
m n p
? ? ? ? ? ?
? ? ? ? ?
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
? ? ? ? ?
? ? ? ?
Question 5:
Solution:
22
(8 6 9) ( 10 8 8 ) a a a a ? ? ? ? ? ?
Collecting like terms and adding them:
22
2
2
2
8 10 6 8 9 8
2 2 1
,
3 ( 2 2 1)
2 2 4
a a a a
aa
Now
aa
aa
? ? ? ? ?
? ? ? ?
? ? ? ? ?
? ? ?
Question 6:
Solution: Collecting like terms and adding them:
(i) 5 7 9
= 12 10
x x y y
xy
? ? ?
?
22
2
3 1 3
(ii)
2 2 2
1 3 3
=
2 2 2
x x x x
xx
? ? ? ?
? ? ?
3
Page 4
Chapter 6: Algebraic Expressions
Page No: 99
Exercise 6A
Question 1:
Solution:
( ) Required sum = (5 7 6 )
= (12 6 )
= 6
i x x x
xx
x
??
?
3 2 4
( ) Required sum =
5 3 5
9 10 12
=
15
7
=
15
ii x x x
x x x
x
?
??
??
2 2 2
2 2 2
2
(iii) Required sum = 5 ( 8 ) 7
= 5 8 7
= 4
a b a b a b
a b a b a b
ab
? ? ?
??
2 2 2 2
2 2 2
2 2 2
31
(iv) Required sum = 5 ( 3 ) ( )
44
31
= 5 3
44
15
= 2 =
22
x x x x
x x x x
x x x
? ? ? ? ?
? ? ?
?
(v) Required sum = 3 4 2 8 5 2 3
= 2 5 3 2 4 8 3
= 4 4 7
x y z y x z x y z
x x x y y y z z z
x y z
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
??
2 2 2 2 2 2
2 2 2 2 2 2
(vi) Required sum = Collecting like term and adding them
= 2 3 5 6 ( 3 4 )
= 2 5 3 3 6 4
= 4
x y x y x y
x x x y y y
x
? ? ? ? ? ?
? ? ? ? ?
22
y ?
2 2 2
2
(vii) Collecting like terms and adding them:
= 5 2 8 8 7 9 3 7 2
= 13 4 14
x x x x x x
xx
? ? ? ? ? ? ? ?
??
? ?
3 2 4 2 3 4 3 7
3 2 3 2 1
()
4 3 4 3 2
ab a b a a b b a b
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
1
( ) Collecting like terms and adding them:
2 4 3 3 5 2 5 7 5
= ( )
3 5 5 4 2 3 2 4 6
2 3 5 4 5 7 3 2 5
= ( ) ( ) ( )
3 4 2 5 2 4 5 3 6
(8 9 30) ( 16 50 35) (18 20 25)
=
12 20 3
viii
a b c a b c a b c
a a a b b b c c c
a b c
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
??
0
29 31 13
=
12 20 30
a b c ??
( x) Collecting like terms and adding them:
8 11 9 3 5 9
= ( )
5 7 4 2 3 5
8 3 11 5 9 9
=
5 2 7 3 4 5
1 2 9
=
10 21 20
i
x y xy x y xy
x x y y xy xy
x y xy
? ? ? ? ? ?
? ? ? ? ?
??
3 2 3 2 2
3 3 2 2 2
32
(x) Collecting like terms and adding them:
3 1 5 5 3 1 3 8
= ( ) ( )
2 4 3 4 5 5 8 15
3 5 1 3 3 5 1 8
=
2 4 4 5 8 3 5 15
1 13 5 4
=
4 20 8 3
x x x x x x x
x x x x x x x
x x x
? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ?
Question 2:
Solution:
( ) 7 ( 8 )
= 7 8
= 15
i xy xy
xy xy
xy
??
?
22
2
(ii) 3
= 4
xx
x
??
?
(iii) (4 5 ) ( )
= 4 5
= 5 6
y x x y
y x x y
yx
? ? ?
? ? ?
?
2 2 2 2
2 2 2 2
(iv) ( 2 ) ( 2 )
= 2 2 (collecting like terms and adding them)
= 4
a b ab a b ab
a a b b ab ab
ab
? ? ? ? ?
? ? ? ? ?
2 2 2 2
2 2 2 2
22
(v) (2 3 +6 ) ( )
= 2 3 6 (collecting like terms and adding them)
= 2 6
x y xy x y
x x y y xy
x y xy
? ? ?
? ? ? ?
??
2
(vi) (2 3 ) ( 3 )
= 2 3 3 (collecting like terms and adding them)
= 2 2
z x y x y z
z z x x y y
z x y
? ? ? ? ?
? ? ? ? ?
? ? ?
Question 3:
Solution:
? ?
? ?
Required sum = ( 3 4 ) (4 9 ) ( 2 3 ) (2 3 4 )
= 4 8 2 3 4
= 2 3 4
a b c a b c b c a a b c
a c a b c
a b c
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ?
??
Question 4:
Solution:
22
22
2
22
22
2
22
2
(8 7 6 ) ( 3 4 )
= 8 3 7 4 6
5 11 5
(2 4 3 ) ( )
2 4 3
3 4
Now,
( 3 4 ) (5 11 5 )
4 14 9
m n p m n p
m m n n p p
m n p
m n p m n p
m m n n p p
m n p
m n p m n p
m n p
? ? ? ? ? ?
? ? ? ? ?
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
? ? ? ? ?
? ? ? ?
Question 5:
Solution:
22
(8 6 9) ( 10 8 8 ) a a a a ? ? ? ? ? ?
Collecting like terms and adding them:
22
2
2
2
8 10 6 8 9 8
2 2 1
,
3 ( 2 2 1)
2 2 4
a a a a
aa
Now
aa
aa
? ? ? ? ?
? ? ? ?
? ? ? ? ?
? ? ?
Question 6:
Solution: Collecting like terms and adding them:
(i) 5 7 9
= 12 10
x x y y
xy
? ? ?
?
22
2
3 1 3
(ii)
2 2 2
1 3 3
=
2 2 2
x x x x
xx
? ? ? ?
? ? ?
3
(iii) 7 7 2 5 5 3
= 14 8 3
x x x y y y
xy
? ? ? ? ? ? ?
??
2 2 2
2
1 2 4 2 1
(iv) 2 5 2 3
3 3 7 7 7
= 6
y y y y y y
yy
? ? ? ? ? ? ? ?
? ? ?
Page: 102
Exercise 6B
Question 1.
Solution: We have,
24
38 aa ? =
2 4 (2 4) 6
(3 8) ( ) 24 24 a a a a
?
? ? ? ? ?
Question 2.
Solution: We have, (
32
65 xx ?? ) =
3 2 (3 2) 5
( 6 5) ( ) 30 30 x x x x
?
? ? ? ? ? ? ? ?
Question 3.
Solution: We have,
2
( 4 ) ( 3 ) ab a bc ? ? ?
2 (1 2) (1 1) 3 2
= ( 4 3) ( ) ( ) = 12 = 12 a a b b a b c a b c
??
? ? ? ? ? ? ?
Question 4.
Solution: We have,
2 3 3 2 3 3 5 4
(2 ) ( 3 ) (2 3) ( ) ( ) 6 a b a b a a b b a b ? ? ? ? ? ? ? ? ? ? ?
Question 5.
Solution: We have,
? ? ? ?
2 2 2 2 3
2 3 2 3 2
3 5 3 5 5
x y xy x x y y x y
? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
Question 6.
Solution: We have,
? ?
3 2 4 2 3 4 3 7
3 2 3 2 1
()
4 3 4 3 2
ab a b a a b b a b
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 7.
Solution: We have,
? ? ? ?
2 2 3 2 2 3 2 2 5 3 2
1 9 1 9 1
27 2 27 2 6
a b a bc a a b b c a b c
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 8.
Solution: We have,
? ? ? ? ? ?
2 2 2 2 2 2 3 3 3
13 7 13 7 91
5 3 5 3 15
ab c a bc a a b b c c a b c
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 9.
Solution: We have,
? ? ? ?
2 2 2 2 3 3
18 25 18 25
15
5 6 5 6
x z xz y x x z z y x z y
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
4
Page 5
Chapter 6: Algebraic Expressions
Page No: 99
Exercise 6A
Question 1:
Solution:
( ) Required sum = (5 7 6 )
= (12 6 )
= 6
i x x x
xx
x
??
?
3 2 4
( ) Required sum =
5 3 5
9 10 12
=
15
7
=
15
ii x x x
x x x
x
?
??
??
2 2 2
2 2 2
2
(iii) Required sum = 5 ( 8 ) 7
= 5 8 7
= 4
a b a b a b
a b a b a b
ab
? ? ?
??
2 2 2 2
2 2 2
2 2 2
31
(iv) Required sum = 5 ( 3 ) ( )
44
31
= 5 3
44
15
= 2 =
22
x x x x
x x x x
x x x
? ? ? ? ?
? ? ?
?
(v) Required sum = 3 4 2 8 5 2 3
= 2 5 3 2 4 8 3
= 4 4 7
x y z y x z x y z
x x x y y y z z z
x y z
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
??
2 2 2 2 2 2
2 2 2 2 2 2
(vi) Required sum = Collecting like term and adding them
= 2 3 5 6 ( 3 4 )
= 2 5 3 3 6 4
= 4
x y x y x y
x x x y y y
x
? ? ? ? ? ?
? ? ? ? ?
22
y ?
2 2 2
2
(vii) Collecting like terms and adding them:
= 5 2 8 8 7 9 3 7 2
= 13 4 14
x x x x x x
xx
? ? ? ? ? ? ? ?
??
? ?
3 2 4 2 3 4 3 7
3 2 3 2 1
()
4 3 4 3 2
ab a b a a b b a b
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
1
( ) Collecting like terms and adding them:
2 4 3 3 5 2 5 7 5
= ( )
3 5 5 4 2 3 2 4 6
2 3 5 4 5 7 3 2 5
= ( ) ( ) ( )
3 4 2 5 2 4 5 3 6
(8 9 30) ( 16 50 35) (18 20 25)
=
12 20 3
viii
a b c a b c a b c
a a a b b b c c c
a b c
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
??
0
29 31 13
=
12 20 30
a b c ??
( x) Collecting like terms and adding them:
8 11 9 3 5 9
= ( )
5 7 4 2 3 5
8 3 11 5 9 9
=
5 2 7 3 4 5
1 2 9
=
10 21 20
i
x y xy x y xy
x x y y xy xy
x y xy
? ? ? ? ? ?
? ? ? ? ?
??
3 2 3 2 2
3 3 2 2 2
32
(x) Collecting like terms and adding them:
3 1 5 5 3 1 3 8
= ( ) ( )
2 4 3 4 5 5 8 15
3 5 1 3 3 5 1 8
=
2 4 4 5 8 3 5 15
1 13 5 4
=
4 20 8 3
x x x x x x x
x x x x x x x
x x x
? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ?
Question 2:
Solution:
( ) 7 ( 8 )
= 7 8
= 15
i xy xy
xy xy
xy
??
?
22
2
(ii) 3
= 4
xx
x
??
?
(iii) (4 5 ) ( )
= 4 5
= 5 6
y x x y
y x x y
yx
? ? ?
? ? ?
?
2 2 2 2
2 2 2 2
(iv) ( 2 ) ( 2 )
= 2 2 (collecting like terms and adding them)
= 4
a b ab a b ab
a a b b ab ab
ab
? ? ? ? ?
? ? ? ? ?
2 2 2 2
2 2 2 2
22
(v) (2 3 +6 ) ( )
= 2 3 6 (collecting like terms and adding them)
= 2 6
x y xy x y
x x y y xy
x y xy
? ? ?
? ? ? ?
??
2
(vi) (2 3 ) ( 3 )
= 2 3 3 (collecting like terms and adding them)
= 2 2
z x y x y z
z z x x y y
z x y
? ? ? ? ?
? ? ? ? ?
? ? ?
Question 3:
Solution:
? ?
? ?
Required sum = ( 3 4 ) (4 9 ) ( 2 3 ) (2 3 4 )
= 4 8 2 3 4
= 2 3 4
a b c a b c b c a a b c
a c a b c
a b c
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ?
??
Question 4:
Solution:
22
22
2
22
22
2
22
2
(8 7 6 ) ( 3 4 )
= 8 3 7 4 6
5 11 5
(2 4 3 ) ( )
2 4 3
3 4
Now,
( 3 4 ) (5 11 5 )
4 14 9
m n p m n p
m m n n p p
m n p
m n p m n p
m m n n p p
m n p
m n p m n p
m n p
? ? ? ? ? ?
? ? ? ? ?
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
? ? ? ? ?
? ? ? ?
Question 5:
Solution:
22
(8 6 9) ( 10 8 8 ) a a a a ? ? ? ? ? ?
Collecting like terms and adding them:
22
2
2
2
8 10 6 8 9 8
2 2 1
,
3 ( 2 2 1)
2 2 4
a a a a
aa
Now
aa
aa
? ? ? ? ?
? ? ? ?
? ? ? ? ?
? ? ?
Question 6:
Solution: Collecting like terms and adding them:
(i) 5 7 9
= 12 10
x x y y
xy
? ? ?
?
22
2
3 1 3
(ii)
2 2 2
1 3 3
=
2 2 2
x x x x
xx
? ? ? ?
? ? ?
3
(iii) 7 7 2 5 5 3
= 14 8 3
x x x y y y
xy
? ? ? ? ? ? ?
??
2 2 2
2
1 2 4 2 1
(iv) 2 5 2 3
3 3 7 7 7
= 6
y y y y y y
yy
? ? ? ? ? ? ? ?
? ? ?
Page: 102
Exercise 6B
Question 1.
Solution: We have,
24
38 aa ? =
2 4 (2 4) 6
(3 8) ( ) 24 24 a a a a
?
? ? ? ? ?
Question 2.
Solution: We have, (
32
65 xx ?? ) =
3 2 (3 2) 5
( 6 5) ( ) 30 30 x x x x
?
? ? ? ? ? ? ? ?
Question 3.
Solution: We have,
2
( 4 ) ( 3 ) ab a bc ? ? ?
2 (1 2) (1 1) 3 2
= ( 4 3) ( ) ( ) = 12 = 12 a a b b a b c a b c
??
? ? ? ? ? ? ?
Question 4.
Solution: We have,
2 3 3 2 3 3 5 4
(2 ) ( 3 ) (2 3) ( ) ( ) 6 a b a b a a b b a b ? ? ? ? ? ? ? ? ? ? ?
Question 5.
Solution: We have,
? ? ? ?
2 2 2 2 3
2 3 2 3 2
3 5 3 5 5
x y xy x x y y x y
? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
Question 6.
Solution: We have,
? ?
3 2 4 2 3 4 3 7
3 2 3 2 1
()
4 3 4 3 2
ab a b a a b b a b
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 7.
Solution: We have,
? ? ? ?
2 2 3 2 2 3 2 2 5 3 2
1 9 1 9 1
27 2 27 2 6
a b a bc a a b b c a b c
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 8.
Solution: We have,
? ? ? ? ? ?
2 2 2 2 2 2 3 3 3
13 7 13 7 91
5 3 5 3 15
ab c a bc a a b b c c a b c
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 9.
Solution: We have,
? ? ? ?
2 2 2 2 3 3
18 25 18 25
15
5 6 5 6
x z xz y x x z z y x z y
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
4
Question 10.
Solution: We have,
? ? ? ?
4 3 3 4 4 5
3 7 3 7 1
14 6 14 6 4
xy x y x x y y x y
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 11.
Solution: We have,
? ? ? ?
2 2 3 3 2 3 2 3 6 6
7 3 6 7 3 6 63
5 2 5 5 2 5 25
x y xy x y x x x y y y x y
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
Question 12.
Solution: We have,
? ? ? ? ? ? ? ? ? ? ? ? ? ?
2 2 2 2 2 2 3 3 3
2 5 6 2 5 6 60 a b ab c bc a a b b c c a b c ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Question 13.
Solution: We have,
? ? ? ? ? ? ? ? ? ? ? ?
2 2 2 2 3 3
4 6 3 4 6 3 72 x xy y x x y y x y ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Question 14.
Solution: We have,
? ? ? ? ? ?
2 2 2 2 2 2 4 3 3
3 15 7 3 15 7
5 7 9 5 7 9
s t st u su s s s t t u u s t u
?? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
Question 15.
Solution: We have,
? ? ? ? ? ?
4 3 2 3 4 2 3 3 7 7
2 14 2 14 3 3
7 7 7 7 4 7
u v uv u v u u u v v v u v
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 16.
Solution: We have,
? ? ? ? ? ? ? ? ? ? ? ? ? ?
2 2 2 3 2 2 2 3 4 5 5
3 3 3 ab b c a c abc a a a b b b c c c a b c ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Question 17.
Solution: We have,
? ? ? ? ? ? ? ?
2 2 2 2 2 2 4 4 4
4 1 4 1 8
66
3 3 3 3 3
x yz y zx xyz x x x y y y z z z x y z
? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Question 18.
Solution: We have:
? ?
? ? ? ?
2 3 2 2 3 2
2 3 1 2
53
2 6 2 6
3 5 3 5
4
5
4
= .
5
a b a b a a b b
ab
ab
??
?? ? ? ? ? ? ?
? ? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
?
? ? ?
?
Verification: When a = 2 and b = 3, we have:
5
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FAQs on RS Aggarwal Solutions: Algebraic Expressions - Mathematics (Maths) Class 7
| 1. What are algebraic expressions? |  |
Ans. Algebraic expressions are mathematical expressions that contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be simplified or evaluated by substituting specific values for the variables.
| 2. How do you simplify algebraic expressions? | |
Ans. To simplify an algebraic expression, combine like terms by adding or subtracting them. Like terms have the same variables raised to the same powers. You can also simplify expressions by using the distributive property or applying the rules of exponents.
| 3. Can you provide an example of simplifying an algebraic expression? | |
Ans. Certainly! Let's simplify the expression 3x + 2y - 4x + 5y. To simplify, we combine the like terms:
3x - 4x + 2y + 5y = -x + 7y
| 4. How do you evaluate algebraic expressions? | |
Ans. To evaluate an algebraic expression, substitute specific values for the variables and perform the operations according to the given expression. Replace each variable with its corresponding value and simplify the expression to obtain a numerical result.
| 5. Can you provide an example of evaluating an algebraic expression? | |
Ans. Of course! Let's evaluate the expression 2x^2 - 3y + 4 for x = 3 and y = 2.
Substituting the values, we get:
2(3)^2 - 3(2) + 4 = 18 - 6 + 4 = 16
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