Algebraic Identities- 2 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

 Page 1


    
                  
                   
 
       
           
Q u e s t i o n : 1 5
Write the following in the expanded form:
i
(a +2b + c)
2
ii
(2a - 3b - c)
2
iii
(-3x + y + z)
2
iv
(m + 2n - 5p)
2
v
(2 + x - 2y)
2
vi
(a
2
 + b
2
 + c
2
)
2
vii
(ab + bc + ca)
2
viii
x
y
+
y
z
+
z
x
2
( )
Page 2


    
                  
                   
 
       
           
Q u e s t i o n : 1 5
Write the following in the expanded form:
i
(a +2b + c)
2
ii
(2a - 3b - c)
2
iii
(-3x + y + z)
2
iv
(m + 2n - 5p)
2
v
(2 + x - 2y)
2
vi
(a
2
 + b
2
 + c
2
)
2
vii
(ab + bc + ca)
2
viii
x
y
+
y
z
+
z
x
2
( )
ix
a
bc
+
b
ca
+
c
ab
2
x
x +2y +4z)
2
xi
(2x - y + z)
2
xii
(-2x + 3y + 2z)
2
S o l u t i o n :
In the given problem, we have to find expended form
i Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
ii Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
iii Given 
We shall use the identity 
(a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
(-3x +y +z)
2
= (-3x)
2
+y
2
+z
2
-2 ×3x ×y +2yz -2 ×(-3x)×z
Hence the expended form of is .
iv Given 
( )
(
Page 3


    
                  
                   
 
       
           
Q u e s t i o n : 1 5
Write the following in the expanded form:
i
(a +2b + c)
2
ii
(2a - 3b - c)
2
iii
(-3x + y + z)
2
iv
(m + 2n - 5p)
2
v
(2 + x - 2y)
2
vi
(a
2
 + b
2
 + c
2
)
2
vii
(ab + bc + ca)
2
viii
x
y
+
y
z
+
z
x
2
( )
ix
a
bc
+
b
ca
+
c
ab
2
x
x +2y +4z)
2
xi
(2x - y + z)
2
xii
(-2x + 3y + 2z)
2
S o l u t i o n :
In the given problem, we have to find expended form
i Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
ii Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
iii Given 
We shall use the identity 
(a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
(-3x +y +z)
2
= (-3x)
2
+y
2
+z
2
-2 ×3x ×y +2yz -2 ×(-3x)×z
Hence the expended form of is .
iv Given 
( )
(
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of  is 
v Given 
We shall use the identity (a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
Hence the expended form of is .
vi Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is .
(vii) Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is .
viii Given 
We shall use the identity 
Here 
By applying in identity we get 
Page 4


    
                  
                   
 
       
           
Q u e s t i o n : 1 5
Write the following in the expanded form:
i
(a +2b + c)
2
ii
(2a - 3b - c)
2
iii
(-3x + y + z)
2
iv
(m + 2n - 5p)
2
v
(2 + x - 2y)
2
vi
(a
2
 + b
2
 + c
2
)
2
vii
(ab + bc + ca)
2
viii
x
y
+
y
z
+
z
x
2
( )
ix
a
bc
+
b
ca
+
c
ab
2
x
x +2y +4z)
2
xi
(2x - y + z)
2
xii
(-2x + 3y + 2z)
2
S o l u t i o n :
In the given problem, we have to find expended form
i Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
ii Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
iii Given 
We shall use the identity 
(a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
(-3x +y +z)
2
= (-3x)
2
+y
2
+z
2
-2 ×3x ×y +2yz -2 ×(-3x)×z
Hence the expended form of is .
iv Given 
( )
(
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of  is 
v Given 
We shall use the identity (a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
Hence the expended form of is .
vi Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is .
(vii) Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is .
viii Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
ix Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is
x Given 
We shall use the identity (a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
Hence the expended form of is 
xi Given 
We shall use the identity (a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
Hence the expended form of is 
xii Given 
Page 5


    
                  
                   
 
       
           
Q u e s t i o n : 1 5
Write the following in the expanded form:
i
(a +2b + c)
2
ii
(2a - 3b - c)
2
iii
(-3x + y + z)
2
iv
(m + 2n - 5p)
2
v
(2 + x - 2y)
2
vi
(a
2
 + b
2
 + c
2
)
2
vii
(ab + bc + ca)
2
viii
x
y
+
y
z
+
z
x
2
( )
ix
a
bc
+
b
ca
+
c
ab
2
x
x +2y +4z)
2
xi
(2x - y + z)
2
xii
(-2x + 3y + 2z)
2
S o l u t i o n :
In the given problem, we have to find expended form
i Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
ii Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
iii Given 
We shall use the identity 
(a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
(-3x +y +z)
2
= (-3x)
2
+y
2
+z
2
-2 ×3x ×y +2yz -2 ×(-3x)×z
Hence the expended form of is .
iv Given 
( )
(
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of  is 
v Given 
We shall use the identity (a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
Hence the expended form of is .
vi Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is .
(vii) Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is .
viii Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is 
ix Given 
We shall use the identity 
Here 
By applying in identity we get 
Hence the expended form of is
x Given 
We shall use the identity (a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
Hence the expended form of is 
xi Given 
We shall use the identity (a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
Hence the expended form of is 
xii Given 
We shall use the identity (a +b +c)
2
= a
2
+b
2
+c
2
+2ab +2bc +2ca
Here 
By applying in identity we get 
Hence the expended form of is .
Q u e s t i o n : 1 6
If a + b + c = 0 and a
2
 + b
2
 + c
2
 = 16, find the value of ab + bc + ca.
S o l u t i o n :
In the given problem, we have to find value of 
Given and 
Squaring the equation , we get
Now putting the value of in above equation we get,
Taking 2 as common factor we get 
Hence the value of is .
Q u e s t i o n : 1 7
If a
2
 + b
2
 + c
2
 = 16 and ab + bc + ca = 10, find the value of a + b + c.
S o l u t i o n :
In the given problem, we have to find value of 
Given 
Multiply equation with 2 on both sides we get,
Now adding both equation  and we get 
We shall use the identity