Division of Algebraic Expressions - Exercise 8.6 | Mathematics (Maths) Class 8 PDF Download

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Question:45
Divide:
x
2
 - 5x + 6 by x - 3
Solution:
x
2
-5x+6
x-3
=
x
2
-3x-2x+6
x-3
=
x(x-3)-2(x-3)
(x-3)
=
(x-3)(x-2)
(x-3)
= x -2
Question:46
Divide:
ax
2
 - ay
2
 by ax + ay
Solution:
ax
2
-ay
2
ax+ay
=
a x
2
-y
2
a(x+y)
=
a(x+y)(x-y)
a(x+y)
= x -y
Question:47
Divide:
x
4
 - y
4
 by x
2
 - y
2
Solution:
 
x
4
-y
4
x
2
-y
2
=
x
2
)
2
- y
2
)
2
x
2
-y
2
=
x
2
+y
2
x
2
-y
2
x
2
-y
2
= x
2
+y
2
Question:48
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Page 2


       
     
      
 
       
 
       
          
       
         
       
       
       
       
          
           
              
          
            
           
Question:45
Divide:
x
2
 - 5x + 6 by x - 3
Solution:
x
2
-5x+6
x-3
=
x
2
-3x-2x+6
x-3
=
x(x-3)-2(x-3)
(x-3)
=
(x-3)(x-2)
(x-3)
= x -2
Question:46
Divide:
ax
2
 - ay
2
 by ax + ay
Solution:
ax
2
-ay
2
ax+ay
=
a x
2
-y
2
a(x+y)
=
a(x+y)(x-y)
a(x+y)
= x -y
Question:47
Divide:
x
4
 - y
4
 by x
2
 - y
2
Solution:
 
x
4
-y
4
x
2
-y
2
=
x
2
)
2
- y
2
)
2
x
2
-y
2
=
x
2
+y
2
x
2
-y
2
x
2
-y
2
= x
2
+y
2
Question:48
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Divide:
acx
2
 + (bc + ad)x + bd by (ax + b)
Solution:
acx
2
+ bc+ad x+bd
(ax+b)
=
acx
2
+bcx+adx+bd
(ax+b)
=
cx(ax+b)+d(ax+b)
(ax+b)
=
(ax+b)(cx+d)
(ax+b)
= cx +d
Question:49
Divide:
(a
2
 + 2ab + b
2
) - (a
2
 + 2ac + c
2
) by 2a + b + c
Solution:
a
2
+2ab+b
2
- a
2
+2ac+c
2
(2a+b+c)
=
a+b)
2
- a+c)
2
(2a+b+c)
=
(a+b+a+c)(a+b-a-c)
(2a+b+c)
=
(2a+b+c)(b-c)
(2a+b+c)
= b -c
Question:50
Divide:
1
4
x
2
-
1
2
x -12 by 
1
2
x -4
Solution:
1
4
x
2
-
1
2
x-12
1
2
x-4
=
1
2
x
1
2
x-4 +3
1
2
x-4
1
2
x-4
=
1
2
x-4
1
2
x+3
1
2
x-4
=
1
2
x +3
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