Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RS Aggarwal Solutions: Algebraic Expressions
RS Aggarwal Solutions: Algebraic Expressions | Mathematics (Maths) Class 7 PDF Download
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Page 1
Question:1
Add the following expressions:
i
5x, 7x, -6x
ii
3
5
x,
2
3
x,
-4
5
x
iii
5a
2
b, -8a
2
b, 7a
2
b
iv
3
4
x
2
, 5x
2
, -3x
2
, -
1
4
x
2
v
x - 3y + 4z, y - 2x - 8z, 5x - 2y - 3z
vi
2x
2
- 3y
2
, 5x
2
+ 6y
2
, - 3x
2
- 4y
2
vii
5x - 2x
2
- 8, 8x
2
- 7x - 9, 3 + 7x
2
- 2x
viii
2
3
a -
4
5
b +
3
5
c, -
3
4
a -
5
2
b +
2
3
c,
5
2
a +
7
4
b -
5
6
c
ix
8
5
x +
11
7
y +
9
4
xy, -
3
2
x -
5
3
y -
9
5
xy
x
3
2
x
3
-
1
4
x
2
+
5
3
, -
5
4
x
3
+
3
5
x
2
-x +
1
5
, -x
2
+
3
8
x -
8
15
Solution:
i
5x + 7x + -6x
= 5x + 7x -6x
= 6x
ii
3
5
x +
2
3
x +
-4
5
x =
9x +10x -12x
15
=
7x
15
iii
5a
2
b +( -8a
2
b) + 7a
2
b
= 5a
2
b - 8a
2
b + 7a
2
b
4a
2
b
iv
3
4
x
2
+ 5x
2
+ -3x
2
+ -
1
4
x
2
=
3
4
x
2
-
1
4
x
2
+ 5x
2
-3x
2
=
1
2
x
2
+ 2x
2
=
5
2
x
2
v Collecting like terms and adding them:
x - 3y + 4z + y - 2x - 8z + 5x - 2y - 3z
= x- 2x + 5x - 3y + y - 2y + 4z - 8z - 3z
= 4x -4y -7z
vi
Collecting like terms and adding them:
2x
2
- 3y
2
+ 5x
2
+ 6y
2
+ (- 3x
2
- 4y
2
)
= 2x
2
+ 5x
2
- 3x
2
- 3y
2
+6y
2
-4y
2
= 4x
2
-y
2
vii
Collecting like terms and adding them:
5x - 2x
2
- 8 + 8x
2
- 7x - 9 + 3 + 7x
2
- 2x
= -2x
2
+8x
2
+ 7x
2
+ 5x - 7x - 2x -8 -9 + 3 = 13x
2
-4x -14
viii
Collecting like terms and adding them:
2
3
a -
4
5
b +
3
5
c + -
3
4
a -
5
2
b +
2
3
c +
5
2
a +
7
4
b -
5
6
c b -
5
2
b +
7
4
b +
3
5
c +
2
3
c -
5
6
c =
(8 -9 +30)a
12
+
(-16 - 50 +35)b
20
+
(18 +20 -25)c
30
=
29
12
a -
31
20
b +
13
30
c
ix
Collecting like terms and adding them:
8
5
( ) ( )
( )
Page 2
Question:1
Add the following expressions:
i
5x, 7x, -6x
ii
3
5
x,
2
3
x,
-4
5
x
iii
5a
2
b, -8a
2
b, 7a
2
b
iv
3
4
x
2
, 5x
2
, -3x
2
, -
1
4
x
2
v
x - 3y + 4z, y - 2x - 8z, 5x - 2y - 3z
vi
2x
2
- 3y
2
, 5x
2
+ 6y
2
, - 3x
2
- 4y
2
vii
5x - 2x
2
- 8, 8x
2
- 7x - 9, 3 + 7x
2
- 2x
viii
2
3
a -
4
5
b +
3
5
c, -
3
4
a -
5
2
b +
2
3
c,
5
2
a +
7
4
b -
5
6
c
ix
8
5
x +
11
7
y +
9
4
xy, -
3
2
x -
5
3
y -
9
5
xy
x
3
2
x
3
-
1
4
x
2
+
5
3
, -
5
4
x
3
+
3
5
x
2
-x +
1
5
, -x
2
+
3
8
x -
8
15
Solution:
i
5x + 7x + -6x
= 5x + 7x -6x
= 6x
ii
3
5
x +
2
3
x +
-4
5
x =
9x +10x -12x
15
=
7x
15
iii
5a
2
b +( -8a
2
b) + 7a
2
b
= 5a
2
b - 8a
2
b + 7a
2
b
4a
2
b
iv
3
4
x
2
+ 5x
2
+ -3x
2
+ -
1
4
x
2
=
3
4
x
2
-
1
4
x
2
+ 5x
2
-3x
2
=
1
2
x
2
+ 2x
2
=
5
2
x
2
v Collecting like terms and adding them:
x - 3y + 4z + y - 2x - 8z + 5x - 2y - 3z
= x- 2x + 5x - 3y + y - 2y + 4z - 8z - 3z
= 4x -4y -7z
vi
Collecting like terms and adding them:
2x
2
- 3y
2
+ 5x
2
+ 6y
2
+ (- 3x
2
- 4y
2
)
= 2x
2
+ 5x
2
- 3x
2
- 3y
2
+6y
2
-4y
2
= 4x
2
-y
2
vii
Collecting like terms and adding them:
5x - 2x
2
- 8 + 8x
2
- 7x - 9 + 3 + 7x
2
- 2x
= -2x
2
+8x
2
+ 7x
2
+ 5x - 7x - 2x -8 -9 + 3 = 13x
2
-4x -14
viii
Collecting like terms and adding them:
2
3
a -
4
5
b +
3
5
c + -
3
4
a -
5
2
b +
2
3
c +
5
2
a +
7
4
b -
5
6
c b -
5
2
b +
7
4
b +
3
5
c +
2
3
c -
5
6
c =
(8 -9 +30)a
12
+
(-16 - 50 +35)b
20
+
(18 +20 -25)c
30
=
29
12
a -
31
20
b +
13
30
c
ix
Collecting like terms and adding them:
8
5
( ) ( )
( )
x +
11
7
y +
9
4
xy +
(
-
3
2
x -
5
3
y -
9
5
xy
)
=
8
5
x -
3
2
x +
11
7
y -
5
3
y +
9
4
xy -
9
5
xy =
1
10
x -
2
21
y +
9
20
xy
(x) Collecting like terms and adding them:
3
2
x
3
-
1
4
x
2
+
5
3
+
(
-
5
4
x
3
+
3
5
x
2
- x +
1
5
)
+
(
- x
2
+
3
8
x -
8
15
)
=
3
2
x
3
-
5
4
x
3
-
1
4
x
2
+
3
5
x
2
- x
2
- x +
3
8
x +
5
3
+
1
Page 3
Question:1
Add the following expressions:
i
5x, 7x, -6x
ii
3
5
x,
2
3
x,
-4
5
x
iii
5a
2
b, -8a
2
b, 7a
2
b
iv
3
4
x
2
, 5x
2
, -3x
2
, -
1
4
x
2
v
x - 3y + 4z, y - 2x - 8z, 5x - 2y - 3z
vi
2x
2
- 3y
2
, 5x
2
+ 6y
2
, - 3x
2
- 4y
2
vii
5x - 2x
2
- 8, 8x
2
- 7x - 9, 3 + 7x
2
- 2x
viii
2
3
a -
4
5
b +
3
5
c, -
3
4
a -
5
2
b +
2
3
c,
5
2
a +
7
4
b -
5
6
c
ix
8
5
x +
11
7
y +
9
4
xy, -
3
2
x -
5
3
y -
9
5
xy
x
3
2
x
3
-
1
4
x
2
+
5
3
, -
5
4
x
3
+
3
5
x
2
-x +
1
5
, -x
2
+
3
8
x -
8
15
Solution:
i
5x + 7x + -6x
= 5x + 7x -6x
= 6x
ii
3
5
x +
2
3
x +
-4
5
x =
9x +10x -12x
15
=
7x
15
iii
5a
2
b +( -8a
2
b) + 7a
2
b
= 5a
2
b - 8a
2
b + 7a
2
b
4a
2
b
iv
3
4
x
2
+ 5x
2
+ -3x
2
+ -
1
4
x
2
=
3
4
x
2
-
1
4
x
2
+ 5x
2
-3x
2
=
1
2
x
2
+ 2x
2
=
5
2
x
2
v Collecting like terms and adding them:
x - 3y + 4z + y - 2x - 8z + 5x - 2y - 3z
= x- 2x + 5x - 3y + y - 2y + 4z - 8z - 3z
= 4x -4y -7z
vi
Collecting like terms and adding them:
2x
2
- 3y
2
+ 5x
2
+ 6y
2
+ (- 3x
2
- 4y
2
)
= 2x
2
+ 5x
2
- 3x
2
- 3y
2
+6y
2
-4y
2
= 4x
2
-y
2
vii
Collecting like terms and adding them:
5x - 2x
2
- 8 + 8x
2
- 7x - 9 + 3 + 7x
2
- 2x
= -2x
2
+8x
2
+ 7x
2
+ 5x - 7x - 2x -8 -9 + 3 = 13x
2
-4x -14
viii
Collecting like terms and adding them:
2
3
a -
4
5
b +
3
5
c + -
3
4
a -
5
2
b +
2
3
c +
5
2
a +
7
4
b -
5
6
c b -
5
2
b +
7
4
b +
3
5
c +
2
3
c -
5
6
c =
(8 -9 +30)a
12
+
(-16 - 50 +35)b
20
+
(18 +20 -25)c
30
=
29
12
a -
31
20
b +
13
30
c
ix
Collecting like terms and adding them:
8
5
( ) ( )
( )
x +
11
7
y +
9
4
xy +
(
-
3
2
x -
5
3
y -
9
5
xy
)
=
8
5
x -
3
2
x +
11
7
y -
5
3
y +
9
4
xy -
9
5
xy =
1
10
x -
2
21
y +
9
20
xy
(x) Collecting like terms and adding them:
3
2
x
3
-
1
4
x
2
+
5
3
+
(
-
5
4
x
3
+
3
5
x
2
- x +
1
5
)
+
(
- x
2
+
3
8
x -
8
15
)
=
3
2
x
3
-
5
4
x
3
-
1
4
x
2
+
3
5
x
2
- x
2
- x +
3
8
x +
5
3
+
1
5
-
8
15
=
1
4
x
3
-
13
20
x
2
-
5
8
x +
4
3
Question:2
Subtract:
i
-8xy from 7xy
ii
x
2
from - 3x
2
iii
(x - y) from (4y - 5x)
iv
(a
2
+ b
2
- 2ab) from (a
2
+ b
2
+ 2ab)
v
(x
2
- y
2
) from (2x
2
- 3y
2
+ 6xy)
vi
(x - y + 3z) from (2z - x - 3y)
Solution:
i
7xy- -8xy
= 7xy+ 8xy
= 15xy
ii
- 3x
2
- x
2
= -4x
2
iii
4y - 5x -
x - y
= 4y - 5x - x + y
= 5y - 6x
iv
(a
2
+ b
2
+ 2ab) - (a
2
+ b
2
- 2ab)
=
a
2
-a
2
+b
2
-b
2
+ 2ab + 2ab Collectingliketermsandaddingthem
= 4ab
v (2x
2
- 3y
2
+ 6xy) - (x
2
- y
2
)
2x
2
- x
2
- 3y
2
+ y
2
+6xy = x
2
-2y
2
+6xy
Collectingliketermsandaddingthem
vi
2z -x -3y
- x -y +3z
= 2z -3z -x -x -3y +y Collectingliketermsandaddingthem
= -z -2x - 2y
Question:3
Subtract (2a - 3b + 4c) from the sum of (a + 3b - 4c), (4a - b + 9c) and (-2b + 3c - a).
Solution:
(a + 3b - 4c) + (4a - b + 9c) + (-2b + 3c - a)
= a + 4a - a + 3b -b -2b -4c +9c + 3c
= 4a + 8c
Now, 4a +8c
- (2a - 3b + 4c)
= 4a - 2a + 3b + 8c - 4c
= 2a + 3b + 4c
Question:4
Subtract the sum of (8m - 7n + 6p
2
) and (-3m - 4n - p
2
) from the sum of (2m + 4n - 3p
2
) and (- m - n - p
2
).
Solution:
(8m - 7n + 6p
2
) + (-3m - 4n - p
2
)
= 8m - 3m - 7n -4n + 6p
2
- p
2
= 5m -11n +5p
2
(2m + 4n - 3p
2
) + (- m - n - p
2
).
x + y + xy , - x - y -
Page 4
Question:1
Add the following expressions:
i
5x, 7x, -6x
ii
3
5
x,
2
3
x,
-4
5
x
iii
5a
2
b, -8a
2
b, 7a
2
b
iv
3
4
x
2
, 5x
2
, -3x
2
, -
1
4
x
2
v
x - 3y + 4z, y - 2x - 8z, 5x - 2y - 3z
vi
2x
2
- 3y
2
, 5x
2
+ 6y
2
, - 3x
2
- 4y
2
vii
5x - 2x
2
- 8, 8x
2
- 7x - 9, 3 + 7x
2
- 2x
viii
2
3
a -
4
5
b +
3
5
c, -
3
4
a -
5
2
b +
2
3
c,
5
2
a +
7
4
b -
5
6
c
ix
8
5
x +
11
7
y +
9
4
xy, -
3
2
x -
5
3
y -
9
5
xy
x
3
2
x
3
-
1
4
x
2
+
5
3
, -
5
4
x
3
+
3
5
x
2
-x +
1
5
, -x
2
+
3
8
x -
8
15
Solution:
i
5x + 7x + -6x
= 5x + 7x -6x
= 6x
ii
3
5
x +
2
3
x +
-4
5
x =
9x +10x -12x
15
=
7x
15
iii
5a
2
b +( -8a
2
b) + 7a
2
b
= 5a
2
b - 8a
2
b + 7a
2
b
4a
2
b
iv
3
4
x
2
+ 5x
2
+ -3x
2
+ -
1
4
x
2
=
3
4
x
2
-
1
4
x
2
+ 5x
2
-3x
2
=
1
2
x
2
+ 2x
2
=
5
2
x
2
v Collecting like terms and adding them:
x - 3y + 4z + y - 2x - 8z + 5x - 2y - 3z
= x- 2x + 5x - 3y + y - 2y + 4z - 8z - 3z
= 4x -4y -7z
vi
Collecting like terms and adding them:
2x
2
- 3y
2
+ 5x
2
+ 6y
2
+ (- 3x
2
- 4y
2
)
= 2x
2
+ 5x
2
- 3x
2
- 3y
2
+6y
2
-4y
2
= 4x
2
-y
2
vii
Collecting like terms and adding them:
5x - 2x
2
- 8 + 8x
2
- 7x - 9 + 3 + 7x
2
- 2x
= -2x
2
+8x
2
+ 7x
2
+ 5x - 7x - 2x -8 -9 + 3 = 13x
2
-4x -14
viii
Collecting like terms and adding them:
2
3
a -
4
5
b +
3
5
c + -
3
4
a -
5
2
b +
2
3
c +
5
2
a +
7
4
b -
5
6
c b -
5
2
b +
7
4
b +
3
5
c +
2
3
c -
5
6
c =
(8 -9 +30)a
12
+
(-16 - 50 +35)b
20
+
(18 +20 -25)c
30
=
29
12
a -
31
20
b +
13
30
c
ix
Collecting like terms and adding them:
8
5
( ) ( )
( )
x +
11
7
y +
9
4
xy +
(
-
3
2
x -
5
3
y -
9
5
xy
)
=
8
5
x -
3
2
x +
11
7
y -
5
3
y +
9
4
xy -
9
5
xy =
1
10
x -
2
21
y +
9
20
xy
(x) Collecting like terms and adding them:
3
2
x
3
-
1
4
x
2
+
5
3
+
(
-
5
4
x
3
+
3
5
x
2
- x +
1
5
)
+
(
- x
2
+
3
8
x -
8
15
)
=
3
2
x
3
-
5
4
x
3
-
1
4
x
2
+
3
5
x
2
- x
2
- x +
3
8
x +
5
3
+
1
5
-
8
15
=
1
4
x
3
-
13
20
x
2
-
5
8
x +
4
3
Question:2
Subtract:
i
-8xy from 7xy
ii
x
2
from - 3x
2
iii
(x - y) from (4y - 5x)
iv
(a
2
+ b
2
- 2ab) from (a
2
+ b
2
+ 2ab)
v
(x
2
- y
2
) from (2x
2
- 3y
2
+ 6xy)
vi
(x - y + 3z) from (2z - x - 3y)
Solution:
i
7xy- -8xy
= 7xy+ 8xy
= 15xy
ii
- 3x
2
- x
2
= -4x
2
iii
4y - 5x -
x - y
= 4y - 5x - x + y
= 5y - 6x
iv
(a
2
+ b
2
+ 2ab) - (a
2
+ b
2
- 2ab)
=
a
2
-a
2
+b
2
-b
2
+ 2ab + 2ab Collectingliketermsandaddingthem
= 4ab
v (2x
2
- 3y
2
+ 6xy) - (x
2
- y
2
)
2x
2
- x
2
- 3y
2
+ y
2
+6xy = x
2
-2y
2
+6xy
Collectingliketermsandaddingthem
vi
2z -x -3y
- x -y +3z
= 2z -3z -x -x -3y +y Collectingliketermsandaddingthem
= -z -2x - 2y
Question:3
Subtract (2a - 3b + 4c) from the sum of (a + 3b - 4c), (4a - b + 9c) and (-2b + 3c - a).
Solution:
(a + 3b - 4c) + (4a - b + 9c) + (-2b + 3c - a)
= a + 4a - a + 3b -b -2b -4c +9c + 3c
= 4a + 8c
Now, 4a +8c
- (2a - 3b + 4c)
= 4a - 2a + 3b + 8c - 4c
= 2a + 3b + 4c
Question:4
Subtract the sum of (8m - 7n + 6p
2
) and (-3m - 4n - p
2
) from the sum of (2m + 4n - 3p
2
) and (- m - n - p
2
).
Solution:
(8m - 7n + 6p
2
) + (-3m - 4n - p
2
)
= 8m - 3m - 7n -4n + 6p
2
- p
2
= 5m -11n +5p
2
(2m + 4n - 3p
2
) + (- m - n - p
2
).
x + y + xy , - x - y -
= 2m -m + 4n -n -3p
2
-p
2
= m + 3n -4p
2
Now, m + 3n - 4p
2
- 5m -11n +5p
2
= -4m +14n -9p
2
Question:5
Subtract the sum of (8a - 6a
2
+ 9) and (-10a - 8 + 8a
2
) from -3.
Solution:
(8a - 6a
2
+ 9)+ (-10a - 8 + 8a
2
)
Collecting like terms and adding them:
8a -10a -6a
2
+ 8a
2
+9 -8 = -2a + 2a
2
+ 1Now, -3 - -2a + 2a
2
+ 1 = 2a - 2a
2
-4
Question:6
Simplify:
i
(5x -9y) - (-7x + y)
ii
x
2
-x -
1
2
x -3 +3x
2
iii
[7 - 2x + 5y - (x - y)] - (5x + 3y - 7)
iv
1
3
y
2
-
4
7
y +5 -
2
7
y -
2
3
y
2
+2 -
1
7
y -3 +2y
2
Solution:
Collecting like terms and adding them:
i
5x + 7x - 9y -y
= 12x -10y
ii
x
2
-
3
2
x
2
-x -
1
2
x +
3
2
= -
1
2
x
2
-
3
2
x +
3
2
iii
7 + 7 - 2x -x - 5x + 5y + y - 3y
= 14 - 8x -3y
iv
1
3
y
2
+
2
3
y
2
-2y
2
-
4
7
y -
2
7
y -
1
7
y +5 -2 +3 = - y
2
- y +6
Question:7
Find the products:
3a
2
× 8a
4
Solution:
3a
2
× 8a
4
= 3× 8 × a
2
× a
4
= 24 × a
(2+4)
= 24a
6
Question:8
Find the products:
-6x
3
× 5x
2
Solution:
-6x
3
× 5x
2
= - 6× 5 × x
3
× x
2
= - 30 × x
(3+2)
= - 30x
5
Question:9
Find the products:
(-4ab) × (-3a
2
bc)
Solution:
(-4ab) × (-3a
2
bc)
= -4 × -3 × a ×a
2
×b ×b ×c = 12 × a
3
b
2
c = 12a
3
b
2
c
Question:10
Find the products:
(2a
2
b
3
) × (-3a
3
b)
Solution:
(2a
2
b
3
) × (-3a
3
b)
= 2 × -3 × a
2
×a
3
×b
3
×b = -6 × a
(2+3)
×b
(3+1)
= -6a
5
b
4
( ) ( )
( )
( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ( ) ) ( ) ( ) ( )
Page 5
Question:1
Add the following expressions:
i
5x, 7x, -6x
ii
3
5
x,
2
3
x,
-4
5
x
iii
5a
2
b, -8a
2
b, 7a
2
b
iv
3
4
x
2
, 5x
2
, -3x
2
, -
1
4
x
2
v
x - 3y + 4z, y - 2x - 8z, 5x - 2y - 3z
vi
2x
2
- 3y
2
, 5x
2
+ 6y
2
, - 3x
2
- 4y
2
vii
5x - 2x
2
- 8, 8x
2
- 7x - 9, 3 + 7x
2
- 2x
viii
2
3
a -
4
5
b +
3
5
c, -
3
4
a -
5
2
b +
2
3
c,
5
2
a +
7
4
b -
5
6
c
ix
8
5
x +
11
7
y +
9
4
xy, -
3
2
x -
5
3
y -
9
5
xy
x
3
2
x
3
-
1
4
x
2
+
5
3
, -
5
4
x
3
+
3
5
x
2
-x +
1
5
, -x
2
+
3
8
x -
8
15
Solution:
i
5x + 7x + -6x
= 5x + 7x -6x
= 6x
ii
3
5
x +
2
3
x +
-4
5
x =
9x +10x -12x
15
=
7x
15
iii
5a
2
b +( -8a
2
b) + 7a
2
b
= 5a
2
b - 8a
2
b + 7a
2
b
4a
2
b
iv
3
4
x
2
+ 5x
2
+ -3x
2
+ -
1
4
x
2
=
3
4
x
2
-
1
4
x
2
+ 5x
2
-3x
2
=
1
2
x
2
+ 2x
2
=
5
2
x
2
v Collecting like terms and adding them:
x - 3y + 4z + y - 2x - 8z + 5x - 2y - 3z
= x- 2x + 5x - 3y + y - 2y + 4z - 8z - 3z
= 4x -4y -7z
vi
Collecting like terms and adding them:
2x
2
- 3y
2
+ 5x
2
+ 6y
2
+ (- 3x
2
- 4y
2
)
= 2x
2
+ 5x
2
- 3x
2
- 3y
2
+6y
2
-4y
2
= 4x
2
-y
2
vii
Collecting like terms and adding them:
5x - 2x
2
- 8 + 8x
2
- 7x - 9 + 3 + 7x
2
- 2x
= -2x
2
+8x
2
+ 7x
2
+ 5x - 7x - 2x -8 -9 + 3 = 13x
2
-4x -14
viii
Collecting like terms and adding them:
2
3
a -
4
5
b +
3
5
c + -
3
4
a -
5
2
b +
2
3
c +
5
2
a +
7
4
b -
5
6
c b -
5
2
b +
7
4
b +
3
5
c +
2
3
c -
5
6
c =
(8 -9 +30)a
12
+
(-16 - 50 +35)b
20
+
(18 +20 -25)c
30
=
29
12
a -
31
20
b +
13
30
c
ix
Collecting like terms and adding them:
8
5
( ) ( )
( )
x +
11
7
y +
9
4
xy +
(
-
3
2
x -
5
3
y -
9
5
xy
)
=
8
5
x -
3
2
x +
11
7
y -
5
3
y +
9
4
xy -
9
5
xy =
1
10
x -
2
21
y +
9
20
xy
(x) Collecting like terms and adding them:
3
2
x
3
-
1
4
x
2
+
5
3
+
(
-
5
4
x
3
+
3
5
x
2
- x +
1
5
)
+
(
- x
2
+
3
8
x -
8
15
)
=
3
2
x
3
-
5
4
x
3
-
1
4
x
2
+
3
5
x
2
- x
2
- x +
3
8
x +
5
3
+
1
5
-
8
15
=
1
4
x
3
-
13
20
x
2
-
5
8
x +
4
3
Question:2
Subtract:
i
-8xy from 7xy
ii
x
2
from - 3x
2
iii
(x - y) from (4y - 5x)
iv
(a
2
+ b
2
- 2ab) from (a
2
+ b
2
+ 2ab)
v
(x
2
- y
2
) from (2x
2
- 3y
2
+ 6xy)
vi
(x - y + 3z) from (2z - x - 3y)
Solution:
i
7xy- -8xy
= 7xy+ 8xy
= 15xy
ii
- 3x
2
- x
2
= -4x
2
iii
4y - 5x -
x - y
= 4y - 5x - x + y
= 5y - 6x
iv
(a
2
+ b
2
+ 2ab) - (a
2
+ b
2
- 2ab)
=
a
2
-a
2
+b
2
-b
2
+ 2ab + 2ab Collectingliketermsandaddingthem
= 4ab
v (2x
2
- 3y
2
+ 6xy) - (x
2
- y
2
)
2x
2
- x
2
- 3y
2
+ y
2
+6xy = x
2
-2y
2
+6xy
Collectingliketermsandaddingthem
vi
2z -x -3y
- x -y +3z
= 2z -3z -x -x -3y +y Collectingliketermsandaddingthem
= -z -2x - 2y
Question:3
Subtract (2a - 3b + 4c) from the sum of (a + 3b - 4c), (4a - b + 9c) and (-2b + 3c - a).
Solution:
(a + 3b - 4c) + (4a - b + 9c) + (-2b + 3c - a)
= a + 4a - a + 3b -b -2b -4c +9c + 3c
= 4a + 8c
Now, 4a +8c
- (2a - 3b + 4c)
= 4a - 2a + 3b + 8c - 4c
= 2a + 3b + 4c
Question:4
Subtract the sum of (8m - 7n + 6p
2
) and (-3m - 4n - p
2
) from the sum of (2m + 4n - 3p
2
) and (- m - n - p
2
).
Solution:
(8m - 7n + 6p
2
) + (-3m - 4n - p
2
)
= 8m - 3m - 7n -4n + 6p
2
- p
2
= 5m -11n +5p
2
(2m + 4n - 3p
2
) + (- m - n - p
2
).
x + y + xy , - x - y -
= 2m -m + 4n -n -3p
2
-p
2
= m + 3n -4p
2
Now, m + 3n - 4p
2
- 5m -11n +5p
2
= -4m +14n -9p
2
Question:5
Subtract the sum of (8a - 6a
2
+ 9) and (-10a - 8 + 8a
2
) from -3.
Solution:
(8a - 6a
2
+ 9)+ (-10a - 8 + 8a
2
)
Collecting like terms and adding them:
8a -10a -6a
2
+ 8a
2
+9 -8 = -2a + 2a
2
+ 1Now, -3 - -2a + 2a
2
+ 1 = 2a - 2a
2
-4
Question:6
Simplify:
i
(5x -9y) - (-7x + y)
ii
x
2
-x -
1
2
x -3 +3x
2
iii
[7 - 2x + 5y - (x - y)] - (5x + 3y - 7)
iv
1
3
y
2
-
4
7
y +5 -
2
7
y -
2
3
y
2
+2 -
1
7
y -3 +2y
2
Solution:
Collecting like terms and adding them:
i
5x + 7x - 9y -y
= 12x -10y
ii
x
2
-
3
2
x
2
-x -
1
2
x +
3
2
= -
1
2
x
2
-
3
2
x +
3
2
iii
7 + 7 - 2x -x - 5x + 5y + y - 3y
= 14 - 8x -3y
iv
1
3
y
2
+
2
3
y
2
-2y
2
-
4
7
y -
2
7
y -
1
7
y +5 -2 +3 = - y
2
- y +6
Question:7
Find the products:
3a
2
× 8a
4
Solution:
3a
2
× 8a
4
= 3× 8 × a
2
× a
4
= 24 × a
(2+4)
= 24a
6
Question:8
Find the products:
-6x
3
× 5x
2
Solution:
-6x
3
× 5x
2
= - 6× 5 × x
3
× x
2
= - 30 × x
(3+2)
= - 30x
5
Question:9
Find the products:
(-4ab) × (-3a
2
bc)
Solution:
(-4ab) × (-3a
2
bc)
= -4 × -3 × a ×a
2
×b ×b ×c = 12 × a
3
b
2
c = 12a
3
b
2
c
Question:10
Find the products:
(2a
2
b
3
) × (-3a
3
b)
Solution:
(2a
2
b
3
) × (-3a
3
b)
= 2 × -3 × a
2
×a
3
×b
3
×b = -6 × a
(2+3)
×b
(3+1)
= -6a
5
b
4
( ) ( )
( )
( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ( ) ) ( ) ( ) ( )
Question:11
Find the products:
2
3
x
2
y ×
3
5
xy
2
Solution:
=
2
3
×
3
5
× x
2
×x ×y ×y
2)
=
2
5
×x
(2+1)
×y
(1+2)
=
2
5
x
3
y
3
Question:12
Find the products:
-3
4
ab
3
×
-2
3
a
2
b
4
Solution:
=
-3
4
×
-2
3
× a ×a
2
×b
3
×b
4
=
1
2
×a
(1+2)
×b
(3+4)
=
1
2
a
3
b
7
Question:13
Find the products:
-1
27
a
2
b
2
×
-9
2
a
3
bc
2
Solution:
=
-1
27
×
-9
2
× a
2
×a
3
×b
2
×b ×c
2
=
1
6
×a
(2+3)
×b
(2+1)
×c
2
=
1
6
a
5
b
3
c
2
Question:14
Find the products:
-13
5
ab
2
c ×
7
3
a
2
bc
2
Solution:
=
-13
5
×
7
3
× a ×a
2
×b
2
×b ×c ×c
2
=
-91
15
a
(1+2)
×b
(2+1)
×c
(1+2)
=
-91
15
a
3
b
3
c
3
Question:15
Find the products:
-18
5
x
2
z ×
-25
6
xz
2
y
Solution:
= -
18
5
×
-25
6
× x
2
×x ×z ×z
2
×y = 15 ×x
(2+1)
×y ×z
(1+2)
= 15x
3
yz
3
Question:16
Find the products:
-3
14
xy
4
×
7
6
x
3
y
Solution:
=
-3
14
×
7
6
× x ×x
3
×y
4
×y =
-1
4
x
(1+3)
×y
(4+1)
=
-1
4
x
4
y
5
Question:17
Find the products:
-7
5
x
2
y ×
3
2
xy
2
×
-6
5
x
3
y
3
Solution:
=
-7
5
×
3
2
×
-6
5
× x
2
×x ×x
3
×y ×y
2
×y
3
=
63
25
×x
(2+1+3)
×y
(1+2+3)
=
63
25
x
6
y
6
Question:18
Find the products:
(2a
2
b) × (-5ab
2
c) × (-6bc
2
)
Solution:
= 2 × -5 × -6 × a
2
×a ×b ×b
2
×b ×c ×c
2
= 60 ×a
(2+1)
×b
(1+2+1)
×c
(1+2)
= 60a
3
b
4
c
3
Question:19
Find the products:
(-4x
2
) × (-6xy
2
) × (-3y)
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( ) ( )
( ) ( )
( ( ) ( ) ) ( )
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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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Nov 22, 2024 Last updated |
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RS Aggarwal Solutions: Algebraic Expressions Notes offer in-depth insights into the specific topic to help you master it with ease.
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RS Aggarwal Solutions: Algebraic Expressions Class 7 Questions
The "RS Aggarwal Solutions: Algebraic Expressions Class 7 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 7 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
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The content of RS Aggarwal Solutions: Algebraic Expressions is prepared as per the latest Class 7 syllabus.
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