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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
Read MoreFAQs on RS Aggarwal Solutions: Algebraic Expressions
| 1. What's the difference between a term and a coefficient in algebraic expressions? |  |
Ans. A term is a single mathematical unit containing variables and constants (like 3x or 5), while a coefficient is the numerical factor multiplying the variable (the 3 in 3x). Understanding this distinction helps students correctly identify and manipulate components within expressions, which is essential for simplifying and solving algebraic problems in Class 7 Mathematics.
| 2. How do I identify like terms and unlike terms when simplifying algebraic expressions? | |
Ans. Like terms have identical variable parts with the same powers (e.g., 2x and 5x), while unlike terms have different variables or exponents (e.g., 2x and 3y). To simplify expressions, combine only like terms by adding or subtracting their coefficients. This fundamental skill directly impacts your ability to reduce complex algebraic expressions into simpler forms for CBSE examinations.
| 3. Why do I keep making mistakes when adding and subtracting algebraic expressions with multiple variables? | |
Ans. The most common mistake is combining unlike terms or forgetting to apply the distributive property with negative signs correctly. Group like terms together first, then perform operations separately for each variable group. Practising with visual worksheets and mind maps available on EduRev helps reinforce this concept and builds accuracy during problem-solving.
| 4. What's the easiest way to understand polynomials and monomials in algebraic expressions? | |
Ans. A monomial contains a single term (3x²), a binomial has two terms (3x + 5), and a polynomial has multiple terms. The classification depends on the number of unlike terms present. This categorisation helps students recognise expression types quickly, which is crucial for selecting appropriate simplification strategies in CBSE Class 7 Maths assessments.
| 5. How should I approach evaluating algebraic expressions by substituting values for variables? | |
Ans. Replace each variable with its given value carefully, maintaining correct operation order-handle exponents first, then multiplication and division, followed by addition and subtraction. Work systematically to avoid calculation errors when substituting into more complex expressions. Referring to solved examples and MCQ tests strengthens your substitution accuracy for real-world application problems.
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