Is it true that we can expand the polynomial

1
4

a−
1
2

b+1

2

using a suitable identity?

Question

Is it true that we can expand the polynomial

1
        4
       
       a−
        1
        2
       
       b+1
     
    2

using a suitable identity?

Accepted Answer

The given expression is

1
        4
       
       a−
        1
        2
       
       b+1
     
    2

.

x+y+z
   ²=x²+y²+z²+2xy+2yz+2zx  …(i)
  We can substitute the variables x, y, z on the left–hand side of this identity (i) with any values and obtain the expanded form by putting the respective values on the right–hand side of the identity (i).Now, we have the following observation.The polynomial

1
        4
       
       a−
        1
        2
       
       b+1
     
    2

is expanded in the following way using the identity (i).Substitute

x=
    a
    4
   
   , y=
    b
    2
   
   , z=1
   in the identity (i) to get the following expansion after simplification.

1
         4
        
        a−
         1
         2
        
        b+1
      
      2
     
     =

a
         4

2
     
     +

−
         b
         2

2
     
     +
      (1)
      2
     
     +2×

a
        4

×
      
       −
        b
        2

+2×
      
       −
        b
        2

×1+2×1×

a
        4

1
         4
        
        a−
         1
         2
        
        b+1
      
      2
     
     =
      
       a
       
        16

2
     
     +
      
       b
       4

2
     
     +1−
      
       ab
      4
     
     −b+
      a
      2

Hence, the given statement is true, we can expand the polynomial

1
        4
       
       a−
        1
        2
       
       b+1
     
    2

using a suitable identityTherefore, the correct option is 1.

Is it true that we can expand the polynomial $14 a − 12 b + 1 2$ using a suitable identity?

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

Is it true that we can expand the polynomial 1 4 a− 1 2 b+1 2 using a suitable identity?

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

Is it true that we can expand the polynomial $14 a − 12 b + 1 2$ using a suitable identity?