RS Aggarwal Solutions: Exercise 6A - Operations on Algebraic Expressions | Mathematics (Maths) Class 8 PDF Download

 Page 1


Q u e s t i o n : 1
Add:
8ab, -5ab, 3ab, -ab
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    8ab -5ab    3ab  -ab
________
   5ab
Q u e s t i o n : 2
Add:
7x, -3x, 5x, -x, -2x
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    7x -3x    5x  -x -2x
_____
  6x
Q u e s t i o n : 3
Add:
3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
3a - 4b + 4c2a + 3b - 8c  a - 6b +  c
___________
6a -7b -3c
Q u e s t i o n : 4
Add:
5x - 8y + 2z, 3z - 4y - 2x, 6y - z - x and 3x - 2z - 3y
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    5x -8y +2z -2x -4y +3z  -x +6y - z   3x -3y -2z   5x -9y +2z
Q u e s t i o n : 5
Add:
6ax - 2by + 3cz, 6by - 11ax - cz and 10cz - 2ax - 3by
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
       6ax -2by + 3cz -11ax + 6by -  cz  -2ax -3by +10cz   - 7ax +  by +12cz
Q u e s t i o n : 6
Add:
2x
3
 - 9x
2
 + 8, 3x
2
 - 6x - 5, 7x
3
 - 10x + 1 and 3 + 2x - 5x
2
 - 4x
3
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
and adding column-wise:
     2x
3
- 9x
2
+  0x +8   0x
3
+ 3x
2
 - 6x -5   7x
3
+ 0x
2
-10x +1 -4x
3
-5x
2
+ 2x +3     5x
3
-11x
2
-14x +7
Q u e s t i o n : 7
Add:
6p + 4q - r + 3, 2r - 5p - 6, 11q - 7p + 2r - 1 and 2q - 3r + 4
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise:
    6p +  4q - r+3 -5p +  0q +2r-6 -7p +11q +2r-1   0p +  2q -3r+4 -6p +17q +0r+0 = -6p +17q
Q u e s t i o n : 8
Add:
4x
2
 - 7xy + 4y
2
 - 3, 5 + 6y
2
 - 8xy + x
2
 and 6 - 2xy + 2x
2
 - 5y
2
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
 and adding column-wise:
4x
2
+4y
2
-7xy -3 x
2
+ 6y
2
-8xy +02x
2
-5y
2
-2xy +67x
2
+5y
2
-17xy +3
Page 2


Q u e s t i o n : 1
Add:
8ab, -5ab, 3ab, -ab
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    8ab -5ab    3ab  -ab
________
   5ab
Q u e s t i o n : 2
Add:
7x, -3x, 5x, -x, -2x
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    7x -3x    5x  -x -2x
_____
  6x
Q u e s t i o n : 3
Add:
3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
3a - 4b + 4c2a + 3b - 8c  a - 6b +  c
___________
6a -7b -3c
Q u e s t i o n : 4
Add:
5x - 8y + 2z, 3z - 4y - 2x, 6y - z - x and 3x - 2z - 3y
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    5x -8y +2z -2x -4y +3z  -x +6y - z   3x -3y -2z   5x -9y +2z
Q u e s t i o n : 5
Add:
6ax - 2by + 3cz, 6by - 11ax - cz and 10cz - 2ax - 3by
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
       6ax -2by + 3cz -11ax + 6by -  cz  -2ax -3by +10cz   - 7ax +  by +12cz
Q u e s t i o n : 6
Add:
2x
3
 - 9x
2
 + 8, 3x
2
 - 6x - 5, 7x
3
 - 10x + 1 and 3 + 2x - 5x
2
 - 4x
3
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
and adding column-wise:
     2x
3
- 9x
2
+  0x +8   0x
3
+ 3x
2
 - 6x -5   7x
3
+ 0x
2
-10x +1 -4x
3
-5x
2
+ 2x +3     5x
3
-11x
2
-14x +7
Q u e s t i o n : 7
Add:
6p + 4q - r + 3, 2r - 5p - 6, 11q - 7p + 2r - 1 and 2q - 3r + 4
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise:
    6p +  4q - r+3 -5p +  0q +2r-6 -7p +11q +2r-1   0p +  2q -3r+4 -6p +17q +0r+0 = -6p +17q
Q u e s t i o n : 8
Add:
4x
2
 - 7xy + 4y
2
 - 3, 5 + 6y
2
 - 8xy + x
2
 and 6 - 2xy + 2x
2
 - 5y
2
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
 and adding column-wise:
4x
2
+4y
2
-7xy -3 x
2
+ 6y
2
-8xy +02x
2
-5y
2
-2xy +67x
2
+5y
2
-17xy +3
Q u e s t i o n : 9
Subtract:
3a
2
b from -5a
2
b
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
and subtracting:
-5a
2
b   3a
2
b - -8a
2
b
Q u e s t i o n : 1 0
Subtract:
-8pq from 6pq
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
                     6pq   -8pq   +                  14pq
Q u e s t i o n : 1 1
Subtract:
-2abc from -8abc
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
     -8abc -2abc  +     -6abc
Q u e s t i o n : 1 2
Subtract:
-16p from -11p
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
  -11p -16p +     5p
Q u e s t i o n : 1 3
Subtract:
2a - 5b + 2c - 9 from 3a - 4b - c + 6
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
     3a -4b - c +6    2a -5b +2c -9 -    +     -    +      a + b -3c +15
Q u e s t i o n : 1 4
Subtract:
-6p + q + 3r + 8 from p - 2q - 5r - 8
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
      p -2q -5r-8 -6p +  q +3r+8 +    -     -   -   7p -3q -8r-16   
Q u e s t i o n : 1 5
Subtract:
x
3
 + 3x
2
 - 5x + 4 from 3x
3
 - x
2
 + 2x - 4
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
and subtracting column-wise:
   3x
3
-x
2
+2x -4  x
3
+3x
2
-5x +4 -    -    +    -  2x
3
-4x
2
+7x -8
Q u e s t i o n : 1 6
Subtract:
5y
4 
- 3y
3
 + 2y
2
 + y - 1 from 4y
4
 - 2y
3
 - 6y
2
 - y + 5
S o l u t i o n :
Arranging the terms of the given expressions in the descending powers of x
and subtracting column-wise:
     4y
4
-2y
3
-6y
2
-y +5   5y
4
-3y
3
+2y
2
+y -1 -     +    -     -   +   -y
4
+ y
3
- 8y
2
-2y +6
Q u e s t i o n : 1 7
Subtract:
4p
2
 + 5q
2
 - 6r
2
 + 7 from 3p
2
 - 4q
2
 - 5r
2
 - 6
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
     3p
2
-4q
2
-5r
2
-6 4p
2
+5q
2
-6r
2
+7 -    -      +      - -p
2
-9q
2
+r
2
-13
Q u e s t i o n : 1 8
Page 3


Q u e s t i o n : 1
Add:
8ab, -5ab, 3ab, -ab
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    8ab -5ab    3ab  -ab
________
   5ab
Q u e s t i o n : 2
Add:
7x, -3x, 5x, -x, -2x
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    7x -3x    5x  -x -2x
_____
  6x
Q u e s t i o n : 3
Add:
3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
3a - 4b + 4c2a + 3b - 8c  a - 6b +  c
___________
6a -7b -3c
Q u e s t i o n : 4
Add:
5x - 8y + 2z, 3z - 4y - 2x, 6y - z - x and 3x - 2z - 3y
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
    5x -8y +2z -2x -4y +3z  -x +6y - z   3x -3y -2z   5x -9y +2z
Q u e s t i o n : 5
Add:
6ax - 2by + 3cz, 6by - 11ax - cz and 10cz - 2ax - 3by
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise, we get:
       6ax -2by + 3cz -11ax + 6by -  cz  -2ax -3by +10cz   - 7ax +  by +12cz
Q u e s t i o n : 6
Add:
2x
3
 - 9x
2
 + 8, 3x
2
 - 6x - 5, 7x
3
 - 10x + 1 and 3 + 2x - 5x
2
 - 4x
3
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
and adding column-wise:
     2x
3
- 9x
2
+  0x +8   0x
3
+ 3x
2
 - 6x -5   7x
3
+ 0x
2
-10x +1 -4x
3
-5x
2
+ 2x +3     5x
3
-11x
2
-14x +7
Q u e s t i o n : 7
Add:
6p + 4q - r + 3, 2r - 5p - 6, 11q - 7p + 2r - 1 and 2q - 3r + 4
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and adding column-wise:
    6p +  4q - r+3 -5p +  0q +2r-6 -7p +11q +2r-1   0p +  2q -3r+4 -6p +17q +0r+0 = -6p +17q
Q u e s t i o n : 8
Add:
4x
2
 - 7xy + 4y
2
 - 3, 5 + 6y
2
 - 8xy + x
2
 and 6 - 2xy + 2x
2
 - 5y
2
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
 and adding column-wise:
4x
2
+4y
2
-7xy -3 x
2
+ 6y
2
-8xy +02x
2
-5y
2
-2xy +67x
2
+5y
2
-17xy +3
Q u e s t i o n : 9
Subtract:
3a
2
b from -5a
2
b
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
and subtracting:
-5a
2
b   3a
2
b - -8a
2
b
Q u e s t i o n : 1 0
Subtract:
-8pq from 6pq
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
                     6pq   -8pq   +                  14pq
Q u e s t i o n : 1 1
Subtract:
-2abc from -8abc
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
     -8abc -2abc  +     -6abc
Q u e s t i o n : 1 2
Subtract:
-16p from -11p
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
  -11p -16p +     5p
Q u e s t i o n : 1 3
Subtract:
2a - 5b + 2c - 9 from 3a - 4b - c + 6
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
     3a -4b - c +6    2a -5b +2c -9 -    +     -    +      a + b -3c +15
Q u e s t i o n : 1 4
Subtract:
-6p + q + 3r + 8 from p - 2q - 5r - 8
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
      p -2q -5r-8 -6p +  q +3r+8 +    -     -   -   7p -3q -8r-16   
Q u e s t i o n : 1 5
Subtract:
x
3
 + 3x
2
 - 5x + 4 from 3x
3
 - x
2
 + 2x - 4
S o l u t i o n :
On arranging the terms of the given expressions in the descending powers of x
and subtracting column-wise:
   3x
3
-x
2
+2x -4  x
3
+3x
2
-5x +4 -    -    +    -  2x
3
-4x
2
+7x -8
Q u e s t i o n : 1 6
Subtract:
5y
4 
- 3y
3
 + 2y
2
 + y - 1 from 4y
4
 - 2y
3
 - 6y
2
 - y + 5
S o l u t i o n :
Arranging the terms of the given expressions in the descending powers of x
and subtracting column-wise:
     4y
4
-2y
3
-6y
2
-y +5   5y
4
-3y
3
+2y
2
+y -1 -     +    -     -   +   -y
4
+ y
3
- 8y
2
-2y +6
Q u e s t i o n : 1 7
Subtract:
4p
2
 + 5q
2
 - 6r
2
 + 7 from 3p
2
 - 4q
2
 - 5r
2
 - 6
S o l u t i o n :
Writing the terms of the given expressions inthesameorder
in the form of rows with like terms below each other and subtracting column-wise:
     3p
2
-4q
2
-5r
2
-6 4p
2
+5q
2
-6r
2
+7 -    -      +      - -p
2
-9q
2
+r
2
-13
Q u e s t i o n : 1 8
What must be subtracted from 3a
2
 - 6ab - 3b
2
 - 1 to get 4a
2
 - 7ab - 4b
2
 + 1?
S o l u t i o n :
Let the required number be x
.
3a
2
-6ab -3b
2
-1 -x = 4a
2
-7ab -4b
2
+1
3a
2
-6ab -3b
2
-1 - 4a
2
-7ab -4b
2
+1 = x
    3a
2
-6ab -3b
2
-1 4a
2
-7ab -4b
2
+1 -     +    +     -  -a
2
+ ab +   b
2
-2
? Required number = -a
2
+ab +b
2
-2
Q u e s t i o n : 1 9
The two adjacent sides of a rectangle are 5x
2
 - 3y
2
 and x
2
 + 2xy. Find the perimeter.
S o l u t i o n :
Sides of the rectangle are l
and b
.
l = 5x
2
-3y
2
b = x
2
+2xy
Perimeter of the rectangle is (2l +2b)
.
Perimeter = 2 5x
2
-3y
2
 + 2 x
2
+2xy                = 10x
2
-6y
2
+2x
2
+4xy     10x
2
-6y
2
   2x
2
         + 4xy    12x
2
-6y
2
+4xyHence, the perimeter of the rectangle is 12x
2
-6y
2
+4xy.
Q u e s t i o n : 2 0
The perimeter of a triangle is 6p
2
 - 4p + 9 and two of its sides are p
2
 - 2p + 1 and 3p
2
 - 5p + 3. Find the third side of the triangle.
S o l u t i o n :
Let a, b and c
be the three sides of the triangle.
? Perimeter of the triangle =(a +b +c)
Given perimeter of the triangle = 6p
2
-4p +9
One side (a
)  = p
2
-2p +1
Other side (b
) = 3p
2
-5p +3
Perimeter = (a +b +c)
6p
2
-4p +9 = p
2
-2p +1 + 3p
2
-5p +3 +c6p
2
-4p +9 -p
2
+2p -1 -3p
2
+5p -3 = c 6p
2
-p
2
-3p
2
+ -4p +2p +5p + 9 -1 -3 = c2p
2
+3p +5 = c
Thus, the third side is 2p
2
+3p +5
.
  
      
  
  
      
  
  
      
  
  
      
  
( )
( ) ( )
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )